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Games andGames and Economic Behavior, 10, 1995, 6-38Econometrica, 68, 2000, 1127-1150International Journal of Game Theory 18, 321--326.@misc{ koller96efficient, author = "D. Koller and N. Meggido and B. von Stengel", title = "Efficient computation of equilibria for extensive two-person games", text = "D. Koller, N. Meggido, and B. von Stengel. Efficient computation of equilibria for extensive two-person games. Games and Economic Behaviour, 14(2):247--259, June 1996.", year = "1996", url = "citeseer.nj.nec.com/koller96efficient.html" }internat. Journal of game theory, 2001http://robotics.stanford.edu/~rwporter/@book{FudTir, AUTHOR = "D. Fudenberg and J. Tirole", TITLE = "Game Theory", PUBLISHER = "MIT Press", YEAR = 1991 }@techreport{roughgarden, author = {T. Roughgarden and E. Tardos}, month = {June}, year = 2001, title = {Bounding the inefficiency of equilibria in nonatomic congestion games}, number = {TR2002-1866}, wasaddress = {Ithaca}, institution = {Cornell} }@inproceedings{kearns2, title="Efficient {Nash} Computation in Large Population Games with Bounded Influence", author="M. Kearns and Y. Mansour", booktitle = "UAI", year = "2002" }@inproceedings{kearns1, author = "M. Kearns and M. Littman and S. Singh", title = "Graphical Models for Game Theory", booktitle = "UAI", year = "2001"}@inproceedings{maids, author = "D. Koller and B. Milch", title = "Multi-Agent Influence Diagrams for Representing and Solving Games", booktitle = "IJCAI", year = "2001" }@inproceedings{graphicalgames, author = "D. Vickrey and D. Koller", title = "Multi-Agent Algorithms for solving graphical games", booktitle = "AAAI", year = "2002" }@article{OsbornePitchik87, author={M.J. Osborne and C. Pitchik}, title={Equilibrium in {Hotelling's} model of competition}, journal={Econometrica}, volume={55}, pages={911-922}, year={1987}}@ W@@@@ -78  %  6 1 1 7 <>_39fidfQimviQSQiQbMQ'e7fidfQimviQSQiQbMQkoLSdi`'e@iQSQiQbMQe5iQSQiQbMQkoLSdi`e iQSQiQbMQkoLSdi`8eJO`YbeOJmJJMMQkkfJUQkOJmJLJkQkSdi`k `dOo^QkiQ^JmYdbkWYfkiQfdimk kMiYfmk kvkiQ^mJL^Qk+kh+MJ^UdiYmW`+kh+MJ^UdiYmW`iQSQiQbMQkoLSdi`weD+kh+MJ^UdiYmW`iQSQiQbMQkoLSdi`+kh+MiQSQiQbMQYO?e/+kh+MMJmQUdiviQSQiQbMQ+kh+MMJmQUdivYO;+kh+MfidfQimviQSQiQbMQ+kh+MfidfQimvYO;e:+kh+MiQSQiQbMQ+kh+MJ^UdiYmW`iQSQiQbMQkoLSdi`w +kh+MiQSQiQbMQ+kh+MMJmQUdiviQSQiQbMQkoLSdi`s+kh+MiQSQiQbMQ+kh+MUJ`QiQSQiQbMQkoLSdi`c+kh+MiQSQiQbMQ+kh+MfidfQimviQSQiQbMQkoLSdi`s+kh+SJ^UdiYmW`e2+kh+SJ^UdiYmW`iQSQiQbMQ?e)+kh+SJ^UdiYmW`iQSQiQbMQkoLSdi`?e,+kh+SMJmQUdiviQSQiQbMQ;+kh+SMJmQUdiviQSQiQbMQkoLSdi`;+kh+SUJ`QiQSQiQbMQkoLSdi`++kh+SfidfQimviQSQiQbMQ;e8+kh+SfidfQimviQSQiQbMQkoLSdi`;eA+kh+SiQSQiQbMQ+kh+SiQSQiQbMQkoLSdi`e +kh+SiQSQiQbMQkoLSdi`8eJ^UdiYmW`J^UdiYmW`Sid`J^UdiYmW`iQSQiQbMQgeJ^UdiYmW`hoQiveJ^UdiYmW`iQSQiQbMQ+MJmQUdivMJmQUdiviQSQiQbMQ'UJ`QUJ`QMJmQUdivUJ`QfidfQimvUJ`QiQSQiQbMQ`kvkJMMQkkdL[QMmk`kvkJMMQkku`^`kvkJMQk`kvkdL[QMmk`kvkhoQiYQk`kvkiQ^JmYdbkWYfkfidfQimvfidfQimviQSQiQbMQ'hoQoQiQSQiQbMQJMMQkk^JvdomeG`kvkOLko``JivYbSd okQiOQSYbQO J^UdiYmW`J^UdiYmW`iQSQiQbMQO+MJmQUdivMJmQUdiviQSQiQbMQG/MJmQUdivUJ`QMJmQUdiv7eFUJ`QUJ`QMJmQUdiv'.UJ`QUJ`QfidfQimv'-UJ`QUJ`QiQSQiQbMQ',fidfQimvUJ`QfidfQimv7eEfidfQimvfidfQimviQSQiQbMQG0iQSQiQbMQJ^UdiYmW`iQSQiQbMQO1iQSQiQbMQMJmQUdiviQSQiQbMQK3iQSQiQbMQUJ`QiQSQiQbMQ;4iQSQiQbMQfidfQimviQSQiQbMQK2nbZN2propertygame-propertygame-propertypropertyidpropertyidzvfR8algorithmalgorithm-referencealgorithm-referencealgorithmidalgorithmalgorithmidlFreferencecategory-referencecategory-referencereferenceidreferenceid~hDreferencegame-referencegame-refS Y NY  Y Y  Y  Y e Y mId LValueObjectGuidObjectNameProperty Value99erdr yKYYYId$ObjectGuidProperty$ObjectNamePropertyѴm@Ѵm@games98MR2GUID$ H+EKu zRppp,,,,,,,* @  QJC<5.'  xqjc\UNG@92+$The learning paper, must assume that a cooperative or adversarial equilibrium exists.Consider worst-case equilibria (worst ratio of NE to the socially optimal outcome) in networkModern Manufacturing supermodular game should be described here Seems too complicated to do us much good.This is another collection of papers. Adding in individual papers that are useful individually.TModern Manufacturing supermodular game should be described here Seems too complicated to do us much good.This is another collection of papers. Adding in individual papers that are useful individually.The learning paper, must assume that a cooperative or adversarial equilibrium exists.Consider worst-case equilibria (worst ratio of NE to the socially optimal outcome) in network games.Title describes it all. No experimental results or results on rate of convergence though. Very easy to implement, however.Not bothering to find this.. Looking at title again, Shapley Value suggests this is about coalitional gamesNever found this reference, but decided after looking at other references that we don't want to bother with differential gamesjust what the title says, doesn't seem to be very interesting to us.Describes how games can be represented efficiently in sequence form, and how Lemke-Howson can be adapted to that efficientlyDescribes ways to play chess more or lessnot bothering with differential gamesdynamic noncooperative game theory is emphatically not normal formcoalition games :( Games and Economic Behavior, 24, 1998Focuses on an algorithm to iteratively find a minimax solution, but does not discuss the details of the algorithm -- references George W. Brown, "Some Notes on Computation of Games Solutions" (1949)These games are far too complicated to easily be reduced to normal formThis is a huge collection of shorter papers. Unfortunately, none of them appear useful to us.In "Models of Strategic Rationality"nLVAL%ddϚΚΚδ ʹʹʹʹʹʹʹ ̊ ̲̊̊̊̊ ˲˲ $ $ʾ D *** need a definition of Sum of players' payoffs is constantSum of players' payoffs is constant Admit pure strategy solutions if and oSum of players' payoffs is constant Admit pure strategy solutions if and only if they have a saddle pSum of players' payoffs is constant Admit pure strategy solutions if and only if they have a saddleSum of players' payoffs is constant Games that can be represented more compactly than with a matrixGames in which the payoff values for each outcome are unique.Games which can be expressed efficiently as trees..Sum of players' payoffs is constant Admit pure strategy solutions if and only if they have a saddle pointRock beats scissors, scissors beat paper, paper beats rock. Generalized matching penniesMultiple equilibria (may?) exist such that one yields higher (or equal) payoffs for all players than anotherWas: common payoff all agents have the same payoffsA 2X2 2-player repeated game, exhibiting interesting equilibrium (0,-1) (0.5, -1) (-1,0)(1,0)Games in which opponents are diametrically opposed but the payoffs do not necessarily add up to something constant.In this game, the NE is a bad prediction because of the huge risk it involves for one of the players.At least one player has a strategy that weakly dominates his other strategies. wb4T& r ;  game-reCgame-refegamegame gamegame game.[igame gamegamegame gamegame game.[is generatogame gamegamegame game game gamegamegamegame gamegamegame gamegame game gamegamegame gamegame game gamegamegamegame game.[is gamegamegamegame game game game game game game game game game game.game gamegame gamegame game.[is generagame gamegame game.[is generator]2game.[is generator]2 game.[is generator]2 ggame.[is generator]2game.[is generator]2game.[is generator]2 game.[is generator]2 g7people 7 people.name* g7 people.id( g7 7 G5([__gameid] = parentid)6 '5__gameid!!! 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O4Sets of Games@uo7+ 74  G4 4 G LVAL This desciptions is probably incomplete: And still needs to be cross-checked with paper A game is parameterized by x_1 and x_2 drawn from interval [0,1] #players = 2 #actions = n each action is a price p_i \in {1,2,..,n} (i.e. assume integer prices up to n ) let f(x,p_1,p_2) = argmin_i ( |x-x_i| + p_i /n) let g_i(x,p_1,p_2) = p_i, if f(x)=i, and 0 otherwise then payoff_i(p_1,p_2) = integral(g_i(x), x=0..1)LVAL lʾxxxxxreferenceSubset Query Superset Query TestCreate form in Design view\m0hs0hs0p;wwo/aw0ͫ0iw0iwiw$p[iwiwCreate form by using wizard\m0hs0hs0p;wwo/aw0ͫ0iw0iwiw$p[iwiwalgorithm-reference Subform\m0hs0hs0p;wwo/aw0ͫ0iw0iwiw$p[iwiwxreferencereference Subform\m0hs0hs0p;wwo/aw0ͫ0iw0iwiw$p[iwiwgame-reference subformform\m0hs0hs0p;wwo/aw0ͫ0iw0iwiw$p[iwiwalgorithmence subformform\m0hs0hs0p;wwo/aw0ͫ0iw0iwiw$p[iwiwxalgorithm-reference Subform1m0hs0hs0p;wwo/aw0ͫ0iw0iwiw$p[iwiw(Generatorseference Subform1m0hs0hs0p;wwo/aw0ͫ0iw0iwiw$p[iwiw(game-reference 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Games.[game-game subset].childidpF"F"pF" F"n 6F"n#game-game subsetpF" ,F"F" F"F"F"pF"F"n 6F"n#game-game subset RF"XF" F"`F"F"pF"F"F"@F"__gameidF" F"F"HF" HF"8F"@F"HF"PF"XF"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"xF"F"pF" PF"F" PF"F" F"z F"F"F"8npF" F"F" F"(F" F" F"0F"F" F" F"F"game-game subset F"8F"PF"PrimaryKeyparentid childidhF"F"lv F"XF"hF"F"F"Fq"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F" F"F"xF"F"'F"game-game subsetPF"F"PF"F"F"8F"F"F"F" F"F"F"F"F" childid F"F" F"[__gameid]F"F"F"F"$F" F"LF" F"(F"F" childidF"PF"F"F"XF"F"F"F" ;tHY i  M A N 4 M  9 <ǑG<LHFFJCöj"B;A_AԀ>>#@#Constant-Sum Games44 d9x@Strict Equilibrium44 h-"<@ +Separable Games11  Friends )tersecIntersection of bounded treewidth and small neighbourhoodOOx !@ !Tractable Pure-Strategy EquilibriaDD w!@!k-Bounded Hypertree-width;; 3u@@G@GAcyclic-Hypergraph Games:: t @G @GAcyclic Graph Games55 sGD@GSmall Neighbourhood55 rG@Gk-Bounded Neighbourhood99 q$`@Markov Games.. 0<!x@!Parallel Network Games88 m@!@Network Games;;, l@@F@%Hotellings Game==, <k@ @>Random Games::, _jb@!z@##All payoffs are unique88 3h @H@>Shapley's Game<<, lg@" @Congestion Games>>, ?e@@>Exponential Game>>, d#@#^@ HUnbalanced Game==, cH@@ (Compound Games<<, ?b@@!Symmetric Games (weak sense)>> 3`r@@ (Dispersion Games3@>,  _Simple Ambush Games ^@/r@Greedy Game99, .]@n@Simple Point Catcher GameGG, W\@@ Simple Inspection GameDD, W[@D@Simplified Poker>>, Z@%@Geometric Games11 Y@z@Morra33,  XN@@HSpite)" W0@0@@>Convergence99, V @ @@>Hero22, U@#@qRock, Paper, ScissorsCC, W T S@@Evolutionarily Stable StrategiesBB R #@ #Complete Opposition55 ,Q@# @+ @Discoordination GamesCC, P@ @ @HContribution Games@@,  O@#Contribution Games* Nl@l@Timing Game-- 0L@#@# @ Dangerous CoordinationDD, Kf@f@Modeller's Dilemma@@, Jf@fV@Small Pig77, I @Dominance-Solvable Equilibrium@@ H#@#Weakly Dominant Strategies<<  GT@=T@=@HBattle of the Bismarck SeaHH, F@@Preemption Games22  EPreemption Games D@*@N-Player Chicken>>, _ C @@qChicken+" @ LVALP v6 Z>  U 7  c G  w V ( l M v W 4  nV~a)pZero-Sum GamespWar of attrition6pUniform Local-Effect Game with clique-Uniform Local-Effect Game!pStag and HarepSecond price auctions formulated as strategic game:pSAT GamespRoad GamepRing structured gamePrisoner's DilemmapPreemption GamespPotential GamespN-Player Prisoner s Dilemma&pModern ManufacturingpMatching PenniespMajority VotingpLocation GamesLocal-Effect GamespInspection GamepHawk and DovepFirst price auctions formulated as strategic games: pDrilling for Oil pDiamond-Type Search Model!pCournot DuopolyCoordination Game   'im@im@property9H@&>>>22222220 @""ʮm@xʮm@category9@>>>22222220 @<m@<m@MSysAccessXML94MR2KeepLocal  T|||<<<<<<<: @Ѵm@śӰm@game9P@&666*******( @ >>22222220 @"yMR2GUID$ ]C)U[ϕ:description ʵM|YFrt( id 4 'FMy,name _0eIйMR2ValidationRuleValidationTextOrientation FilterOrderByOrderByOnNameMapDefaultViewGUIDColumnWidthColumnOrderColumnHiddenDescription FormatCaptionInputMaskDefaultValueRequiredAllowZeroLengthDisplayControlIMEModeIMESentenceMode$UnicodeCompressionE    UD-F$_?_@_A_B_D_E_F_G_H_I_J_ KLMNOPBQBRBSBTBVBWBXB YB ZB [B \B ]B^B_B`BaBbBcBdBeBfBgBhBiBjBkBlBmBnBoB pB! up "9 8 ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up 9 8 ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up 9 8 9 ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up 8 8 9 ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up 8 8 9 ;$ o`zzi '\?Rbw_x6mXVra*NH+lm@lm@reference944444444442 'im@im@property9H@&>>>22222220 @""ʮm@xʮm@category9@>>>22222220 @<m@<m@MSysAccessXML94MR2KeepLocal  T|||<<<<<<<: @Ѵm@śӰm@game9P@&666*******( @ _?_@_A_B_D_E_F_G_H_I_J_ KLMNOPBQBRBSBTBVBWBXB YB ZB [B \B ]B^B_B`BaBbBcBdBeBfBgBhBiBjBkBlBmBnBoB pB!+lm@lm@reference944444444442 'im@im@property9H@&>>>22222220 @""ʮm@xʮm@category9@>>>22222220 @<m@<m@MSysAccessXML94MR2KeepLocal  T|||<<<<<<<: @Ѵm@śӰm@game9P@&666*******( @ Zero-Sum Games<<,  @vN@ (Partial Dispersion Games3HF, @ +@ Selfish Dispersion GamesFF, @J@]Weak Dispersion Games3EC, @%@Common Preference Dispersion GamesPP, r LVAL"""""""" " " ""MR2ODBCTimeoutMaxRecordsRecordLocksRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLQ <       gL۪H4n  U'ςO>;{y@Vv@gameL~Jޘ)9g'ςO>;{includedi J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{descriptionUE]=,J&ZbN'ςO>;{generateHDlLA(R,s'ςO>;{coding priorityŗ`AjD&*,'ςO>;{coding completeLVAL\T:DFzH i?FzFz Fz@FzbT <FzFzFz*FzJFzbFzFzFzFzFzFzFzFz Fz@FzXFzxFzFzFzFzFzFzFzFzFzFzFzFzFzFzFzF"zFz*FzJFzbFzFzFzFzFz                 game.namegamegame.description+game.extensible-actiongame.generategame.gameidgame.entered by!game.is generator+game.extensible-playergame.included'game.coding completeFz  Fz FzFz FzS|-x@FzFz0FzcFzcFzc*Fzcs- JFzcbFzc<}sFzcFzc oFzcsFzcC game Fz    Fz FzFz Fz8L)x@GeneratorsFz FzFz FzFz FzFz FzFz @Fz Fz  Fz0 Fz 8 Fz` Fz h Fz Fz Fz Fz  Fz FzFzFz/game.[extensible-action]Fz Fz@Fz!game.[entered by] Fz%game.[is generator]8 Fz/game.[extensible-player]h FzFz+game.[coding complete] Fz FzcXFzcXFzcX*FzcXJFzcbFzc Fzc@FzceFzc@ Fzc game Fz Fz Fz Fz Fz Fz *Fz Fz JFz Fz bFz Fz Fz Fz Fz Fz Fz Fz Fz FzFzFzFz Fz@Fz Fz8 Fzh FzFz Fz FzXFzFz Fz8Fz`FzFzFzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFz FzFzxFzFzHFz FzFz FzFz $PFzFz FzFz $PFzFz`PFzFz  PFzFz  PFzFz  PFzFz  PFzFz Fzz Fz8FzFzhFzFz FzFz(FzFz `Fz FzFz0FzFz@FzFzPFz@Fz`FzxFzpFzFzFz Fz Fz(Fz `FzFzFzFz@FzxFzFzP(FzFzFzFzFzFzFzFzFzFzFzFz(Fz`FzFzFzFz@FzxFzFzFzgame PFzxFz Fz#FztobeincludedgamePrimaryKeypeoplegame gameidFzFzv FzFz0bTFzXFzXFqzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzXFzFz FzFzFz@FzgameFz@Fz PFz@Fz PFz@FzFzFzFzhFz0FzxFzFzFzFzFz Fz&%ga e3卐 f ̏L8 nK ʥ U 7  c G  \\\\\\ @+Neutrally Stable Strategies3?= W#B@+Centipede Game00 hT@+@(Bertrand Oligopoly with Constant Unit Cost and Linear Demand Functionstt, n@%$@(Linear Cournot DuopolyDD, ,@%Simple Ambush Game364 #@!Coordination Games4 ~0@2x2 Symmetric Games375 }|@@Minimum Effort GamesBB, _v!@!k-Bounded Treewidth Games;; pGd@G@>Soccer Game99, i!@!All NE's have index 177 ff@!#Tree Structured Game66 a@@Traveler's Dilemma@@, _ prFirst price auctions formulated as strategic gamesL@First price auctions formulated as strategic gamesTTHHx YL&& ;;;;͠ d 4 v U   j 8 888I,gameI,game II,game I,I,game I,I,game I,I,gameI,gameI,gameI,game GeneratGenerators%%% Generators%%% Generators%%% Generators%%% GeneratGeneratGenerators%%%Generators%%% Generators%%% GeneratGeneratGenerators%%% Generators%%% Generators%%% GeneratGeneratGenerators%%% GeneratGenerators%%% Generators%%% GeneratGeneratGenerators%%% GeneratGenerators%%% Generators%%% GeneratGeneratGenerators%%% GeneratGenerators%%% Generators%%% GeneratGeneratGenerators%%%Generators%%% Generators%%% GeneratGeneratGenerators%%% Generators%%% Generators%%% GeneratGenerators%%% Generators.gameid0 gGenerators.name. g  GG  game_1.name* 'G  game.name( 'Ggame-game subset111 Ggame Ggamegame_1%% Ggame_1game-game subsetP@oI= Ggamegame-game subsetN@oE9 G game_1.name* gG game.name( greference###   G  G([__id] = referenceid)5 '__id Oalgorithm-referenceGAMUT ReferencesWW7   G  G([__id] = referenceid)5 '__id Ogame-referenceGAMUT ReferencesMM-   G  G wYN66r1Y Y  gameidreferenceidjj467f44f4f468f4f4f46?f4YYYY+Y$gamegame-reference gameidPrimaryKey.referencegame-referencereferenceid+,-./0123  456789":";"<'='>'?+@+A+B/C/D   /L|m@L|m@category-reference9FFFFFFFFFFD +lm@lm@reference9:@ &@@@44444442 @'im@im@property9H@&>>>22222220 @""ʮm@xʮm@category9@>>>22222220 @<m@<m@MSysAccessXML94MR2KeepLocal  T|||<<<<<<<: @Ѵm@śӰm@game9P@&666*******( @ >>22222220 @""ʮm@xʮm@category9@>>>22222220 @<m@<m@MSysAccessXML94MR2KeepLocal  T|||<<<<<<<: @Ѵm@śӰm@game9P@&666*******( @ / v/ 0 ?0 u0 2 3 @3 5 8 A8 B8 C8 D9 E: F; G< H= I> ? @ NA OA B PB C SC ^C pC zC D TF VF aG H XI YI J ZL \M ]N `P bQ dR fS mS S U oU sU V qV W rY wY Z x[ y\ ] ^ ` a c 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D. / 0 1 -1 J1 3 K3 6 *6 +6 46 96 L7 < < > ? n? o? p? q? rJ RJ SJ TL WL XL YL ZL [L \L ]L ^L _L `L aL bL cL dL gM 0M 1M 6M 7M 8M :M MM NM OM PM QM fM N N N N N N N O UP hQ iQ jQ kQ lR mY xY ~Y Y Y Y Z sZ tZ uZ vZ wZ yZ zZ {Z |\ \ \ \ \ \ \ \ \ \ ] ] ] ] ] a a b c c f f f f g g g h h h h h h i i i j m o o o p p p p p p p p p p p p p LVALv6 Z>  U 7  c G  ))pZero-Sum GamespWar of attrition6pUniform Local-Effect Game with clique-Uniform Local-Effect Game!pStag and HarepSecond price auctions formulated as strategic game:pSAT GamespRoad GamepRing structured gamePrisoner's DilemmapPreemption GamespPotential GamespN-Player Prisoner s Dilemma&pModern ManufacturingpMatching PenniespMajority VotingpLocation GamesLocal-Effect GamespInspection GamepHawk and DovepFirst price auctions formulated as strategic gamesTwo countries are choosing levels of arms. Payoffs are based on the cost of the level of arms and the relationship between the country's level and the level of the opponent country.LVALme.[is generator] Fz$FzFzFzFzFz@Fz Fz Fz0Fz @ FzXFz PFzXFzFz0Fz8FzpFz8FzFzFz LVALv6 Z>  U 7  c G  ))pZero-Sum GamespWar of attrition6pUniform Local-Effect Game with clique-Uniform Local-Effect Game!pStag and HarepSecond price auctions formulated as strategic game:pSAT GamespRoad GamepRing structured gamePrisoner's DilemmapPreemption GamespPotential GamespN-Player Prisoner s Dilemma&pModern ManufacturingpMatching PenniespMajority VotingpLocation GamesLocal-ESome finite number of players N are exert effort in search for trading partners. Any trader's probability of finding another particular trader is proportional to his own effort and the total effort of others. Effort, of course, comes at some cost.n!x@!@ Parallel Network GamesDD, LVALb Games in which a strategy profile can be found by deleting a (weakly) dominated strategy from the strategy set of one of the players, recalculating to find which remaining strategies are (weakly) dominated, deleting one of them, and continuing the process until only one strategy remains for each player. Also called "Iterated Dominance Equilibrium"Elaborate story designed to introduce interated-dominant eq: "Set in the South Pacific in 1943. Rear Admiral Kimura has been ordered to transport Japanese troops across the Bismarck Sea to New Guinea, and Admiral Kenney wants to bomb the troop transports. Kimura must choose between a shorter northern route or a longer southern route to New Guinea, and Kenney must decide where to send his planes to look for the Japanese. If Kenney sends his planes to the wrong route he can recall them, but the number of days of bombing is reduced." May not be any special reason to generate this game instead of other zero-sum games, but including it since it was mentioned seperately.Players are two oil firms which own similar tracts of land which may or may not bear oil. Each firm is given a signal at time 0 with some information about the common value v of the land. Drilling costs are c, and the discount factor for waiting for the other firm to drill before drilling is d. If one firm drills at time 0 then the other can condition whether or not it will drill on the results. Game ends immediately if neither firm drills at time 0.NLVAL# . ` ɼɼɼɼɼȨȨȨȨȨȨȨ>v lGenerate a payoff matrix a, Generate pThe paper describes characteristics of a ** Kevin, can you fill in the auGenerate (uniformly) random payoffs for each outcome for player 1 and then negate these to obtain the payoffs for player 2.Generate in same manner as the uniform local-effect game except with F_{a,a'} = F_{a,a''} for all a,a',a''Generate a random graphical game using a tree structure as the underlying graph.Create a graphical game using the road structured graph and a subgame either random or Rock, Paper, Scissors.Create a random graphical game using a graph structure which is a ring of rings.Create a matrix of the appropriate size for the number of players and actions and fill in payoffs (uniformly) at random.Parametrize by exponential parameter b, generate 2x2 matrix: (-2^b, 2^b+1) (0,0) (0,0) (2,-1)Same as bidirectional local-effect game except use only linear functions.like normal LEG except generate only one function for each pair of edges (a, b) and (b, a) and store at bothUnclear if this is extensible at allSee the paper, page 14. Description is too complex to type here. (5 players, 2 actions - many entries)Generate payoff matrix for 2 player game b, b a, d d, a c, cGenerate payoff matrix for two players c, c a, b b, a d, d where a > b > c > dGenerate a payoff matrix a, a d, b b, d c, c where a > b > c > dPayoff function based on v, c, and d can be set up as a triple integral as detailed in the Milgroms and Roberts paper. One possible idea for getting this into normal form: each player has options of "drill immediately" "drill conditioned on whether other player drills immediately" and "do not drill at all" from the start and payoffs are calculated for each combination of these choices according to who would end up drilling and the function given. Could make a standard function and parametrize on c, v, and d perhaps.L5@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@     ? nL WM QP hZ {\ h          .L co      L [\     L gZ |   J R \       Y ~ Z t c  g             L _  /   h i p   i        ! 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D9  E:  F;  G<  H=  I>N ?h @M NAM OAN BM PBN C? pCJ SCL ^CZ zC\ DJ TF VFL aG\ HL XIL YIh JL ZLL \ML ]NL `PL bQL dRM fSR mS\ Sf U? oUZ sUc V? qVN W? rYZ wY\ ZY x[Z y\Y ]Y ^Y `] ag c\ co d< e< f3 fm g. k7 k> l0 ma mb na r  s  t  u  v  w  x  y  z  |g ~f Y h i  j f ] ] ] ] M              ;m@;m@MSysRelationships8DDDDDDDDDDB ;m@;m@MSysQueries888888888886 ;m@;m@MSysACEs822222222220 ;m@;m@MSysObjects888888888886 ;m@K~n@MSysDb9@X:::......., @;m@;m@Relationships8<<<<<<<<<<: ;m@;m@Databases844444444442 ;m@;m@Tables8.........., LVALhD0D0 ?H 0 4 !  d people.id peoplepeople.name |詠o@g$ Vg$/ӯopeople`@ k2Zo@;~sq_cSets of Games~sq_cCombo18 P Xg$tl g$   people    x  8@HPXx@  @ `H@  z   8j$  X   d 0    @  people( @ PrimaryKeyidP v h@P  q                             ( peoplePrimaryKey hh h @ dern MModern Manufacturing<@ @ (Modern ManufacturingXXB6**,e+"r ON2MtMTMLCLKKWKK JIIH:GL4ED>3CC pz@Introduction to tutorial on the theory of the firm and industry equilibriumMartin J. Osbornevvvc  oCongestion games and potentials reconsideredVoorneveld, Borm, and van Megen^@eYY8  nb@Global Games: Theory and ApplicationStephen Morris and Hyun Song Shin___< y@iAn Efficient, Exact Algorithm for Solving Tree-Structured Graphical GamesLittman, Kearns, (Singh?)|||a  l@iDominance Solvable English Multi-item AuctionsKamecke, Ulrich@3cWWF  k`@iEfficient Computation of Behavior StrategiesBernhard von Stengel@3fZZD  2Backwards induction in the centipede gameJohn Broome and Wlodek Rabinowiczz@dXX5  *An Introduction to Game Theory (draft of Chapter 3)Martin OsborneOOO?  hR@iLecture Notes from Columbia University Economics W4415: Game TheoryLevent Kokesenlll[  gWeb Games and Strategic Behavior: Recipes for Interactive LearningCharkes A. Holt@ Ck__N  fEvolutionary Game TheoryJorgen W. Weibull777$  eMultiagent Q-LearningJunling Hu and Michael Wellmann@MAA!  dMarkov Games as a Framework for Multi-Agent Reinforcment LearningMichael Littman^^^M 9Rational and convergent Learning in Stochastic GamesMichael Bowling and Manuela Velosoddd@  bl@iThe Price of Anarchy is Independent of the Network TopologyTim RoughGardendddS xWors- Case EquilibriaElias Koutsoupias and Christos PapadimitriouOOO! lV@Quantal Response Equilibria for Normal Form GamesR.D. McKelvey, T.R. PalfreyfffI rB@ A Simple Adaptive Procedure Leading to Correlated EquilibriumS. Hart, A. Mas-ColellmmmU 5In proc 18-th ICML, 2001Friend-or-Foe Q-learning in general-sum games.Michael Littmanqqq`000  ]Dispersion GamesT. Grenager, R. Powers, Y. Shohamh@K??  pGame Theory and Experimental GamesAndrew Coleman>>>. YGames of StrategyMelvin Dreshner... A Gentle Introduction to Game TheorySaul Stahl<<<0 ZGeometric Games and Their ApplicationsW. H. Ruckle@@@2 mAn Introduction to Linear Programming and Matrix Game TheoryM. J. FryerUUUH nAlgorithms for GamesAdelson-Velsky, Arlazarov, DonskoyDDD Computational Models of GamesAnne Condon666)  U _Omniscience and Omnipotence: How they may Help - of Hurt - in a GamePPPP MDeception in 2 X 2 GamesSteven J. Brahms@B66$  RA Note on Evolutionarily Stable Strategies in Asymmetric Animal ConflictReinhard SeltenH@"qeeT  jBraithwaite's Arbitration SchemeD. Marc Kilgour===, iPrisoner's Dilemma - Recollections and ObservationsAnatol RapoportPPP?  OThe Economics of Modern Manufacturing: Technoly, Strategy, and OrganizationMilgrom and Roberts@"xllW  LVALЂ ʼ Z>  U 7  c G  Two players, both can either hunt stag or huntGames in which a strategy profile can be found by deleting a (weakly) dominated strategy from the strategy set of one of the players, recalculating to find which remaining strategies are (weakly) dominated, deleting one of them, and continuing the process until only one strategy remains for each player.Two players, both can either hunt stag or hunt hare. If both hunt stag they will catch a stag together, split it, and have a high payoff. If one hunts stag and the other hare, the one hunting stag alone will not be able to catch it and will have a lower payoff, while the one hunting hare will have a reasonably high payoff. If both hunt hare, they will both catch the hare but not as much as if only one of them hunted hare. Two (unique?) NE are (stag, stag) Two players, both can either hunt stag or hunt hare. If both hunt stag they will catch a stag together, split it, and have a high payoff. If one hunts stag and the other hare, the one hunting stag alone will not be able to catch it and will have a lower payoff, while the one hunting hare will have a reasonably high payoff. If both hunt hare, they will both catch the hare but not as much as if only one of them hunted hare. Two (unique?) NE are (stag, stag) and (hare, hare).Two players are involved in a disbute over an object. The value of the object to player i is vi > 0. Time is modeled as a continuous variable (although I don't see why we couldn't model is as a discrete variable to make life simpler) starting at 0. Each player chooses when to concede the object to the other player. If the first player to concede does so at time t, the other player receives the object at that time. If both concede simultaneously the object is split between them and each receives payoff vi / 2. One unit of utility is subtracted from the payoff of both players for every unit of time that goes by. 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Randomly choose a highest payoff value and place this payoff in some subset of the maximal dispersion outcomes. Set all other outcomes to have lower payoffs. %GG###ΐ ͐ O = C CJ^UdiYmW`\D6m@D6m@referenceproperty-referenceVVVVVVVVVVV WS//m@f//m@algorithm-reference9@ QTTTHHHHHHHF @Re*m@y,m@algorithm9@ Q@@@44444442 @M]S4&m@ɶ4&m@queue9@Q888,,,,,,,* @G!m@?{!m@property-reference9@ERRRFFFFFFFD @@1Km@Mm@game-property9@EHHH<<<<<<<: @;am@ m@game-category9@:HHH<<<<<<<: @5F~m@~m@gpeoplealgorithmalgorithmentered bypeopleidb^R>,peoplegamegampeoplealgorithmalgorithmentered bypeopleidb^R>,peoplealgorithmalgorithmentered bypeopleidb^R>,peoplealgorithmalgorithmentered bypeopleidb^R>,peoplpeopprioritygamegamecoding prioritypriorityID`\L.&tobeincludedgamegameincludedtobeincludedidb^F6.gamegame-game subset2game-game subsetchildidgamegameidznfX8gamegame-game subset1game-game subsetchildidgamegameidznfX8gamegame-game subsetgame-game subsetparentidgamegameidznfV6peoplealgorithmalgorithmentered bypeopleidb^R>,peoplegamegameentered bypeopleidNJ>*"peoplereferencereferenceassigned topeopleidd`T>,referencegame-referencegame-referencereferenceidreferenceidnX<referencealgorithm-referencealgorithm-referencereferenceidreferenceidlFgamegame-referencegame-referencegameidgamegameidnbZN2algorithmalgorithm-referencealgorithm-referencealgorithmidalgorithmalgorithmidlF*+!ONGNM~MML LKKvJ oIHGQFEE#ED-D[#AiAAz JGame Theory Topics: Incomplete Information, Repeated Games, and N-Player GamesEvelyn C. Fink, Scott Gates, Brian D. HumesZ kModels of Strategic RationalityReinhard Selten<<<+ hGame Theory As a Theory of Conflict ResolutionA. Rapaport (Ed.)MMM: A Game of Fair DivisionVincent Crawford@ A55#  FCognition and Behavior in Normal-Form Games: An Experimental StudyMiguel Costa-Gomes, Vincent Crawford, and Bruno Broseta@3N  EAn Incomplete Cooperation Structure for a Voting Game Can Be Strategically StableYossi Feinbergv@ "ymm]  DSubjective Reasoning in Dynamic GamesYossi Feinberg@MAA1  PDF Core Equivalence Theorems for Infinite Convex GamesMondererR@YMMC  d@ Weighted Majority Games Have Many mu-ValuesMondererMMMC HValues of Smooth Non-Atomic Games: The Method of Multilinear Approximation in The Shapley ValueMonderer, Neyman}}}k 8@iTeam Games As Models of Intergroup ConflictsGary Bornstein & Roger HurwitsdddD `@ web page 1""""  UnpublishedSimulated annealing of games equilibria.M. Pearson, P. La-MurafffN### \@ Efficient Computation of Equilibria for Extensive Two-Person GamesDaphne Koller, Nimrod Megiddo, Bernhard von StengelZ  < EC 2003A polynomial time nash equilibrium algorithm for repeated games.M. Littman, P. Stonewwwa oL@On the np-completeness of finding an optimal strategy in games with common payoffsChu and J. Halpern~~~j The Complexity of two-person zero-sum games in extensive form.D. Koller, N. MeggidoaaaJ  9Nash propagation for Loopy Graphical GamesOrtiz and KearnsHHH6  8Ryan's webpageComputing Equlibria for Two-Person Games.B. von StengelF@maaQ&&&  N@Computation of Equilibria in Finite GamesR. McKelvey and A. McLennan^^^A  6A Continuation Method for Nash Equilibria In Structured gamesBen Blum, Chris Shelton, Daphne Koller@}qqI  {@Bounding the inefficiency of equilibria in nonatomic congestion gamesT. Roughgarden and E. Tardos{{] }p@Efficient Nash Computation in Large Population Games with Bounded InfluenceM. Kearns and Y. Mansour}}c W6@Graphical Models for Game TheoryM. Kearns and M. Littman and S. Singh__8 ^@Multi-Agent Influence Diagrams for Representing and Solving GamesD. Koller and B. MilchqqY T@Multi-Agent Algorithms for solving graphical gamesD. Vickrey and D. KollerddJ 3@Equilibrium in Hotelling's model of competitionM.J. Osborne and C. PitchikddG >@ Stability in CompetitionH. Hotelling>>0 q@R.W. RosenthalA Class of Games Possessing Pure-Strategy {Nash} Equilibriacc& h@Potential GamesD. Monderer and L.S. ShapleyEE' >@Complexity Results about Nash EquilibriaConitzer, SandholmTT@ @Multi-Agent Reinforcement Learning: Theoretical Framework and an AlgorithmHu, Wellmanoob  A General Theory of Equilibrium Selection in GamesHarsanyi, SeltonbookVP> PN        egNobodyAlex Jenn EugeneKevin  LVAL game-category Subform1h2& n@n@Tables~sq_fgame-category subformf2& en@en@Tables~sq_fgameD2& 8xn@zn@Tables~sq_fcategory-reference subform1r2& xVn@xVn@Tables~sq_fcategory-reference subformp2& Έ4n@Έ4n@Tables~sq_fcategoryL2& DR+n@ S+n@Tables~sq_falgorithm-reference Subform1t2& Nm@Nm@Tables~sq_falgorithm-reference Subformr2& /~-zn@-zn@Tables~sq_falgorithmN2& E-n@E-n@Tables~sq_creference~sq_cproperty-reference subform2& @D-n@@D-n@Tables~sq_creference~sq_cgame-reference subform22& E-n@bE-n@Tables~sq_creference~sq_ccategory-reference subform2& @D-n@E-n@Tables~sq_creference~sq_calgorithm-reference subform2& m@m@Tables~sq_cproperty-reference~sq_cpropertyid~2& =2n@=2n@Tables~sq_cproperty~sq_cproperty-reference 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on@A@AccessLayout94MR2KeepLocal T& zz:::::::8 @7m@m@~sq_cproperty-reference~sq_cpropertyid9@s4MR2KeepLocal Tznnnnnnl `3>sm@>sm@reference9@@@@44444442 @/%ԫm@%ԫm@~sq_calgorithm-reference Subform~sq_creferenceid9@4MR2KeepLocal T `.Nm@Nm@~sq_falgorithm-reference Subform9 @4MR2KeepLocal Tnbbbbbb` `-Nm@Nm@algorithm-reference Subform9@ldddXXXXXXXV @ ҂^m@c/Vv@Admin9 @d8,,,,,,,,,* LVALr NMMMThe interests of the players are diametrically opposed but it is not necessary that the sums of payoffs for every outcome are equal. Is this exactly the same thing as discoordination games in the generator section????? If so, can get rid of this one and keep the generator.Agents have common payoffs or should coordinate to get their highest payoffs. . . Seems to be a bit of a mixup about which of these is the correct definition, so I am going with the def in Rasmusen's text which comes with how to generate Have three equilibria: - two symmetric equilibria in pure strategies - one symmetric equilibrium in mixed strategiesTime is discrete, if one player grabs dollar first he keeps it, if both grab at once they have to pay a penalty of one dollar each. Has asymetric eqilibria in pure strategies and symmetric equilibria in mixed strategies.Government wishes to aid a pauper if he searches for work but not otherwise, and a pauper searches for work only if he cannot receive government aid.Similar to Prisoner's Dilemma except that if both prisoner's deny the charges, there is not enough evidence to convict either. Will still choose a bad NE, but now because of only weakly dominant strategies.Another elaborate story designed to illustrate another dominance-solvable game: "Two pigs are put in a Skinner box with a special panel at one end and a food dispenser at the other. When a pig presses the panel at a utility cost of two units, ten units of food are dispensed. One pig is dominant, and if he gets to the dispenser first, the other pig will only get his leavings, worth one unit. If, instead, the small pig arrives first, he eats four units, and even if they arrive at the same time the small pig gets three units." NE is dominent pig presses, other pig waits. 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G. . GLVALД@ f {tmf_XQJC<5.'   Y  Y  Y Id LValue@misc{ littman-efficient, author = "Michael L. Littman and Michael Kearns", title = "An Efficient, Exact Algorithm for Solving Tree-Structured Graphical Games", url = "citeseer.nj.nec.com/543070.html" }abstract is at http://www.wiwi.uni-bonn.de/sfb/papers/abstracts/bonnsfa447.html Kamecke, Ulrich (1994): Dominance Solvable English Multi-item Auctions, SFB 303, Universitt Bonn, Discussion Paper No. A-447@misc{ stengel-efficient, author = "B. von Stengel", title = "Efficient computation of behavior strategies", text = "B. von Stengel (1996a), Efficient computation of behavior strategies. Games and Economic Behavior 14, 220--246.", url = "citeseer.nj.nec.com/vonstengel96efficient.html" }http://users.ox.ac.uk/~sfop0060/pdf/backwards%20induction.pdfhttp://www.columbia.edu/~lk290/gameug.htmIntroduces Wolf Learning Algorithm Tested on repeated versions of matching pennies, rock-paper-sci@misc{ littman-efficient, author = "Michael L. Littman and Michael Kearns", title = "An Efficient, Exact Algorithm for Solving Tree-Structured Graphical Games", url = "citeseer.nj.nec.com/543070.html" }abstract is at http://www.wiwi.uni-bonn.de/sfb/papers/abstracts/bonnsfa447.html Kamecke, Ulrich (1994): Dominance Solvable English Multi-item Auctions, SFB 303, Universitt Bonn, Discussion Paper No. A-447@misc{ stengel-efficient, author = "B. von Stengel", title = "Efficient computation of behavior strategies", text = "B. von Stengel (1996a), Efficient computation of behavior strategies. Games and Economic Behavior 14, 220--246.", url = "citeseer.nj.nec.com/vonstengel96efficient.html" }http://users.ox.ac.uk/~sfop0060/pdf/backwards%20induction.pdfhttp://www.columbia.edu/~lk290/gameug.htmIntroduces Wolf Learning Algorithm Tested on repeated versions of matching pennies, rock-paper-scissors, grid world and soccerJournal of Computer and System Sciences and STOC 2002K[.| > N {  g T ArtFooterjin_queuein queuedin_queue_Labelin queue_Labelmtitledtitle_Labelm authorsd authors_Labelm assigned_toassigned tod assigned_to_Labelassigned to_Labeld Label8mText9mText10fLine11bibtexBlobDeltaPropDataR~ 11\}  n.0ZY?0 K}C0BlobDeltaPropDataj12q}#*Ё }C__SRP_0@ }Blob  TypeInfo?BlobDelta<PropData; 3PU+}CBlob l TypeInfoxBlobDeltau5  !"#$%&'()*+,-6012<?9>H@ABCFlGiJKLNOfQRSTeWXYZ[\]^_`abcdefghkjmnsqrtuyz|}7PIwkBlob v TypeInfoBlobDelta6 LVAL*N  ŃŃŃŃŃŃŃŃŃŃŃŃ Ht333n@T4n@~sq_freference9@ @4MR2KeepLocal TJ>>>>>>< `Y9n@9n@referencegame-reference9PPPPPPPPPPN Xn@n@referencecategory-reference9XXXXXXXXXXV W|n@|n@referenceproperty-reference9XXXXXXXXXXV Ve5n@e5n@referencealgorithm-reference9ZZZZZZZZZZX T2n@2n@propertyproperty-reference9VVVVVVVVVVT Sn@n@categorycategory-reference9VVVVVVVVVVT Q6An@6An@gamegame-category9DDDDDDDDDDB PkĒn@kĒn@gamegame-property9DDDDDDDDDDB O@n@@n@gamegame-reference9FFFFFFFFFFD Mn@n@algorithmalgorithm-reference9ZZZZZZZZZZX WS//m@E n@algorithm-reference9@TTTHHHHHHHF @Re*m@EUn@algorithm9J@i@@@44444442 @G!m@Cn@property-reference9@LRRRFFFFFFFD @@1Km@9n@game-property9@:HHH<<<<<<<: @;am@n@game-category9@4HHH<<<<<<<: @5F~m@]n@game-reference9@DJJJ>>>>>>>< @/L|m@mn@category-reference9@&RRRFFFFFFFD @+lm@ijUn@reference9@>O@@@44444442 @'im@jKUn@property9 @>>>>22222220 @""ʮm@]f:Un@category9@A>>>22222220 @<m@<m@MSysAccessXML94MR2KeepLocal  T|||<<<<<<<: @Ѵm@.1Un@game9"@ >666*******( @ H@ABClFiJKLNOfQRSTeWXYZ[\]^_`abcdefghkjmnsqrtuyz|}ijMSysDb 13CB0 12CB0 11CB0 10CB0 8CB0 2CB0 9CB0 0CB0 7CB0 1CB0 3CB0 5CB0 18CB0 4CB0 20CB0 21CBLabel11-BF5A-4A33-8F7B-9B8CF0AFBCBD}" DocClass=Form_refer00 Name="games" HelpContextID="0" VersionCompati000" CMG="CAC88BC351C751C751C751C7" DPB="9496D51D y Q )   @4 )@8ttt@< 1vvv 18CB0 5CB0 3CB0 1CB0 7CB0 0C@PAYrU h$ LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{8L)x@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding completeTLVALкϺϺϺϺϺϺϺϺϺϺϺϺϺϺϺϺϺϺϺϺϺϺ84 0 0000000000000000̀ ˂ ˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂˂ " """""" Ʉ2 6dž&vtitled title_LabelPropData PropDataCopy%Blob \TypeInfo;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up 9 9 ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up 8 9 ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wSELECT [game-game subset].parentid, [game-game subset].childid FROM [game-game subset]; SELECT [game-game subset].parentid, [game-game subset].childid FROM [game-game subset]; SELECT [game-game subset].parentid, [game-game subset].childid FROM [game-game subset]; SELECT [game-game subset].parentid, [game-game subset].childid FROM [game-game subset]; SELECT [game-game subset].parentid, [game-game subset].childid FROM [game-game subset]; SELECT [game-game subset].parentid, [game-game subset].childid FROM [game-game subset]; game.gameid=[game-game subset].childid[game-game subset].parentid=game_1.gameidgame_1.gameid=[game-game subset].childidgame.gameid=[game-game subset].parentidSELECT [game-game subset].parentid, [game-game subset].childid FROM [game-game subset]; SELECT [game-game subset].parentid, [game-game subset].childid FROM [game-game subset]; game.gameid=[game-game subset].parentidSELECT [game-game subset].parentid, [game-game subset].childid FROM [game-game subset]; SELECT [game-game subset].parentid, [game-game subset].childid FROM [game-game subset]; (((reference.[assigned to])=5) AND ((reference.[in queue])=True))(((reference.[assigned to])=4) AND ((reference.[in queue])=True))(((reference.[assigned to])=2) AND ((reference.[in queue])=True))(((reference.[assigned to])=1) AND ((reference.[in queue])=True))(((reference.[assigned to])=3) AND ((reference.[in queue])=True))game.gameid=[game-reference].gameid=У$NTNMMZMMLL6LLKKXKKJV #JIItIP* ȸHm4HGǐGNGGFFbF^F0EE~éHDC3BAAD@Chicken B!P@Force-Vulnerable Games88 A&n@Threat-Vulnerable Games99 @d@ d@ No dominant strategies88 ?l@#l@#Pure Coordination33 :)@Uniform Local-Effect Game with cliqueGG "@ Bidirectional Local-Effect Game with all F linearSS ?; @ Weak Equilibrium22 p:Game has only one equilibriumUnique EquilibriumSS??9)8Always has a PSNEPure-strategy equilibriumNN33 7Perfect Information  6@ Perfect Equilibria Exist0 5@#@#Pareto ordered / Strictly Better Equilibria ExistSS 4"@!No pure-strategy Nash when N > 3BB 3@R@%No Pure-Strategy Equilibria== 2@z@ Trembling Hand Perfect Equilibria ExistII  1Dominated Strategies Removed( 0/n@H@Symmetric Games (strong sense)@@  .Supermodular Games 8) @Polymatrix Games( @ Non-Braithwaite Games- f@!Mixed-Motive Games* &@Classical Matrix Game- f@ Improper Braithwaite Games2 Graphical Games  &*@fComplete Opposition+ @Compact Representation. f@Braithwaite Games) #6@6@Anti-Braithwaite Games88 Dominant Strategy  !blah blah  blah  new game 2  new game <@T@SAT Games)@Ring structured game(@Road Game++ > 6@Potential Games#tiPreemption Games@f@Grab the DollarOO>2&&_fInspection Game~@y@ Inspection Game@/#oMajority Voting@y@Majority Voting@/#NStag and HareStag and Hare$!AModern ManufacturingModern Manufacturing2Drilling for OilDrilling for Oil*Arms RacesArms RacesDiamond-Type Search ModelDiamond-Type Search Model<!!!!uSupermodular Games2@ Supermodular Games:&&oBertrand Oligopoly@yBertrand Oligopoly:&&Cournot Duopoly@yCournot Duopoly4##3Location Games@yLocation Games2""LWar of attritionWar of attrition*e(Second price auctions formulated as strategic gameSecond price auctions formulated as strategic gamen::::uFirst price auctions formulated as strategic gamesFirst price auctions formulated as strategic gamesn::::Matching PenniesB@ @ Matching PenniesB0$ erN-Player Prisoner s Dilemma@$@N-Player Prisoner s DilemmallL@44Hawk and Dove(@aJ@4Hawk and DoveJJ;/##76H LVAL | |||||h r1 Generate a payoff matrix with 8 choices for player 1 and 4 for player 2. Since this matrix is zero-sum, I will only list the payoffs for player 1 here .. Subtract these from 0 to get the payoffs for player 2:Generate a payoff matrix with 8 choices for player 1 and 4 for player 2. Since this matrix is zero-sum, I will only list the payoffs for player 1 here .. Subtract these from 0 to get the payoffs for player 2: a a 0 0 a/2 0 b/2 (b-a)/2 a/2 (a-b)/2 b/2 0 a/2 0 -b/2 (-a-b)/2 0 -a 0 -a 0 (-a-b)/2 0 (-a-b)/2 a/2 (a+b)/2 -b/2 0 0 (b-a)/2 0 Generate a matrix with payoffs b, b c, a a, c d, d Where a > b > c > d Certain variations can also be generated as mentioned in Hawk and Dove. These have more restrictions. Generating for more than 2 players is under n-player chicken.Generate 2-player 4 by 4 payoff matGenerate a matrix with payoffs b, b c, a a, c d, d Where a > b > c > d Certain variations can also be generated as mentioned in Hawk and Dove. These have more restrictions. Generating for more than 2 players is under n-player chicken.Can't really generate dreastically different verGenerate a matrix with payoffs b, b c, a a, c d, d Where a > b > c > d Certain variations can also be generated as mentioned in Hawk and Dove. These have more restrictions. Generating for more than 2 players is under n-player chicken.Can't really generate dreastically different versions of this. Generate payoff matrix for two players with three choices. b, b a, c c, a c, a b, b a, c a, c c, a b, b where a > b > c and a + c = b Generally, a = 1, b = 0, c = -1 in which case is zero-sum. pH;Uniform Local-Effect Game!Prisoner's DilemmaLocal-Effect GamesCoordiBattle of the Sexes@"@3'nLVAL~D>p`  j? ppppH p !pppppppp  d property.idpropertyproperty.namepppp pm@ppi``p8'i`!`p8'i``propertyppp pp2n@K~sq_cproperty-reference~sq_cpropertyidp pxp ppppp8'p8'property p`p phppp p`p p p8p@pHpPpXpppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppxpp p Pp p`p p pz P pPph p)p8 pp p p8 p dp p08 p@ p8 pp p pproperty p pproperty idPrimaryKey ppv pppp`p`qp`p`p`p`p`p`p`p`p`p`p`p`p`p`p`p`p`p`p`p`p`p`p`p`p`p`p`p`p@p ppPp0ppH ppropertyPrimaryKeyPpH pp ppPp`pPp pPpp p RϝbONNRNNMcMML t JL  @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ !"#$%&'()*+,-./0123I I I  I I I I I I I I I I I II I!I"I#I$I%I&I'I(I)I*I+I,I-I.I/I0I1I2I3I4I5I6I7I8I9I:IC  456789":";"<'='>'?+@+A+B/C/D/E5F5G5H;I;J;K@L@M@NGOGIGIMIMIMIRIRIRIWIWI WI                      @@@@$NashProp$:@$KLS Algorithm for Graphical Games=: Regret Matching8$@Simulated Annealing/: 8@Littman-Stone Repeated NE5:t LP For zero-sum Games! t l@CSP Discretization for Graphical Games> t Obvious from description.Local Search for epsilon NashP1  @Wilson-Govindan Continuation Method; td@Iterative Method for Solving Zero Sum GamesC Inner Ray Approximation# Monotone Inner Hyperplane Approximation3 tLemke-HowsonLemke-Howson& tMyopic best response@Myopic best responseB, xtThis is my third algorithmD@2&  xtalg2  t algorithm1here is how algorithm 1 worksA  (+'ϬϗpT+zNM~MMLKJJILIHHGFHFEEDDBDCúB?BAADAA@DwL d@ESufficiency Conditions for Nash Equilibrium in N-Person Differential GamesStalford, LeitmannjjV Differential GamesAvner Friedman.. Some Topics in Two-Person GamesLloyd Shapley::+ vAn Iterative Method of Solving a GameJ. Robinson>>1 XIterative Solution of Games by Ficticious PlayG. W. BrownGG: Existence of Nash Equilibrium in N-Person Games without QuasiconcavityNishimura, FriedmanggR UExotic Phenomena in Games and Duopoly ModelsDavid RandDD8 mNash Equilibrium in Oligopoly Games with Monotone Best ResponsesXavier VivesZZL nNash Equilibria with Strategic ComplementaritiesXavier VivesJJ< KA General Theory of Equilibrium Selection in GamesHarsanyi, SeltonPP> VGames and DecisionsLuce, Raiffa-- The Strategy of ConflictThomas Schelling66$ FDynamic Games of InnovationJennifer Reinganum;;'  Useless for what we wantStability in CompetitionHarold Hotelling\\J000 |Computing Supergame EquilibriaJudd, Yeltekin, ConklinCC* JEquilibrium Points in Nonzero-Sum N-Person Supermodular GamesTopkisQQI Monotone Comparative StrategiesMilgrom and ShannonMonotone Comparative StrategiesMilgrom, Shannonssa@@++ mMixed Equilibria in Games of Strategic ComplementsEchenique and EdlinMixed Equilibria in Games of Strategic ComplementsEchenique and EdlinSS>> !The Set of Nash Equilibria of a Supermodular GameLin ZhouThe Set of Nash Equilibria of a Supermodular GameLin ZhouzGG== mRationalizability, Learning, and Equilibrium in GaMilgrom and RobertsRationalizability, Learning, and Equilibrium in GaMilgrom and RobertsSS>> MA course in microeconomic theoryDavid M. KrepsA Course in Microeconomic TheoryDavid M. Krepsnn^<<,, aAn experimental study of N-person iterated prisoneX. Yao and P. DarwenAn experimental study of N-person iterated prisoneX. Yao and P. DarwenTT>> iA continuation method for nash equilibria in Struc>>>>>>> PGame Theory and AgentsStefan J. JohanssonGame Theory and AgentsStefan J. JohanssonddO77"" ISelection Criteria in Coordination Games: Some ExpCooper, DeJong, Forsynthe, RossSelection Criteria in Coordination Games: Some ExpCooper, DeJong, Forsynthe, Ross__>> EPure Nash Equilibria: Hard and Easy GamesTo appear in TARK IXGeorge Gottlob,Gianluigi Greco,Francesco ScarcelloPure Nash Equilibria: Hard and Easy GamesGeorge Gottlob,Gianluigi Greco,Francesco ScarcelloW5 mbGame TheoryGuillermo OwenGame TheoryGuillermo OwenDD4'' 'Game TheoryFudenburg and TiroleGame TheoryFudenburg, TiroleMM:-- Equilibrium points in N-person gamesNashEquilibrium points in N-person gamesNashbb\6600 MA course in game theory&@Osborne, RubensteinA course in game theoryOsborne, Rubensteinrr]DD/# eLocal-Effect Games:@Leyton-Brown, TennenholtzLocal-Effect GamesLeyton-Brown, TennenholtzttYEE* ref42 authors  reference123 authors third thingref5blah ref4 reference3something elsesomethingP LVAL` {&hI( ^ ?  r Z > + n O , l G )  v 5  sY=`E(0000)pZero-Sum Games )Welfare GamepWar of attrition6pUniform Local-Effect Game with clique-Uniform Local-Effect Game!!)Unbalanced Game#)Tree Structured Game)Traveler's DilemmapStag and Hare-)Soccer Game)Small Pig)Simplified Poker)Simple Point Catcher Game!)Simple Inspection Game 3Simple Ambush Game%)Shapley's GamepSecond price auctions formulated as strategic game:pSAT Games)Rock, Paper, ScissorspRoad GamepRing structured game()Random GamesPrisoner's DilemmapPotential Games+)Parallel Network GamespN-Player Prisoner s Dilemma&)N-Player Chicken*)Network Games)Morra pModern Manufacturing)Modeller's Dilemma3Minimum Effort GamespMatching PenniespMajority VotingpLocation GamesLocal-Effect Games 3Linear Cournot DuopolypInspection Game))Hotellings Game)Hero pHawk and Dove,)Grid Game)Greedy GamepGrab the Dollar7)FriendspFirst price auctions formulated as strategic games:")Exponential Game pDrilling for Oil)Dispersion GamesDispersion games in which agents' preferences may allign with either the dispersion ordering or with a set of exogenous preferences. For example, an "anti-battle-of-the-sexes" scenario in which a man and his ex-wife both wish to attend one of two parties, one of which is more desirable, but bother prefer not to encounter each otherLVALstill no idea on whether weighted majority games might be useful to us but I would guess not(June 1993). The internal problem of collective action that arises when groups, as opposed to individuals, are in conflict cannot be studied in the context of two-person games that treat the competing groups as unitary players. Traditional N-person games are also too restrictive for this purpose, since they ignore the conflict of interests between the groups. Because the intergroup conflict motivates the need for intragroup collective action, and the groups' respective success in mobilizing collective action determines the outcome of the intergroup competition, the intergroup and intragroup levels should be considered simultaneously. This paper: (a) proposes to model intergroup conflicts as team games (Palfrey & Rosenthal, 1983; (b) offers an initial taxonomy for this class of games; and (c) illustrates some applications for strategic analyses of intergroup conflict and political interactions. N..  1gameidgamegameidgame.gameidP:.&&   generategamegenerategame.generate\ Hawk and Dove@@-!J LVALЂ f fN..Two prisoners are caught and asked to confess. Each prisoner chooses to cooperate or defect. Defect is the dominant strategy for both players and thus forms an equilibrium, even though it is the only pure out come which is not Pareto optimal.- three (or more) players 1, 2, 3 vote on three (or more) candidates A, B, C - each has utility of - three (or more) players 1, 2, 3 vote on three (or more) candidates A, B, C - each has utility - three (or more) players 1, 2, 3 vote on three (or more) candidates A, B, C - each has utility of 2 for first choice player winning, utility 1 for second choice, utility 0 for third choice, and each (at least in this example) have different orderings of the candidates- player 1 is an agent with strategies shirk or work - player 2 is a principal with strategies inspect or not inspect - working costs g for agent and produces v for principal - inspecting costs h for principal - principal must pay agent w unless has evidence that the agent did not work (i.e. agent played shirk and principal played inspect) - mixed strategy Nash: probability agent shirks is h/w, probability that principal inspects is g/w"Each of n people chooses whether or not to become a political candidate, and if so which position to take. There is a continuum of citizens,- three (or more) players 1, 2, 3 vote on three (or more) candidates A, B, C - each has utility of 2 for first choice player winning, utility 1 for second choice, utility 0 for third choice, and each (at least in this example) have different orderings of the candidates- player 1 is an agent with strategies shirk or work - player 2 is a principal with strategies inspect or not inspect - working costs g for agent and produces v for principal - inspecting costs h for principal - principal must pay agent w unless has evidence that the agent did not work (i.e. agent played shirk and principal played inspect) - mixed strategy Nash: probability agent shirks is h/w, probability that principal inspects is g/w NLocation Games@y"" ' No pure-strategy Nash when N > 3"No pure-strategy Nash when N > 3V( N00.....  !referenceidgame-referencereferenceidgame-referetproperty tproperty.id/ 3tproperty.name3 3Cournot Duopoly@y## vcPγ<)))))))))))))))) ͌͌͌͌͌͌͌͌͌͌͌y  e eeeeeeeeeeeeeee ;$ o`zziB ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>B 9 A 8 A 8 A ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>A 8 A 8 A 8 A ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>A 8 A 8 A 8 A ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>A 8 A 8 A 8 A ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>A 8 A 8 A 8 A ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>A 8 A 8 A 8 A ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>A 8 A 8 A 8 A ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>A 8 A 8 A 8 A ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>A 8 A 8 A 8 A ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>A 8 A 8 A 8 A ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>A 8 A 8 A 8 A ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>A 8 A 8 A 8 A ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>A 8 A 8 A 8 A ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>A 8 A 8 A 8 A ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>A 8 A 8 A 8 A ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>A 8 A 8 A 8 A ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>A 8 @9 @9 @;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>@9 >;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up >8 7 8 7 ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up 7 9 39 3;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up 38 / 8 / ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up / 9 . 8 . ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up . 9 -9 -;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up -8  аO3G 3333 33ppWar of attritionUniform Local-Effect Game!pSecond price auctions formulated as strategic game:Prisoner's DilemmapN-Player Prisoner s Dilemma&pMatching PenniespLocation GamesLocal-Effect GamespHawk and DovepFirst price auctions formulated as strategic games:Coordination GameBidirectional Local-EBertrand Oligopoly@y&& O3G ,,,, pppWar of attritionUniform Local-Effect Game!pSecond price auctions formulated as strategic game:Prisoner's DilemmapN-Player Prisoner s Dilemma&pMatching PenniespLocation GamesLocal-Effect GamespHawk and DovepFirst price auctions formulated as strategic games:Coordination GameBidirectional Local-ESupermodular Games2@ && LVAL ( k ^ Q D --Generate a matrix a, w b, x c, yFor two players, generate a matrix: 0, For two players, generate a matrix: 0, For two players, generate a matrix: 0, For two players, generate a matrix: 0, -H For two players, generate a matrix: 0, -H For two players, generate a matrix: 0, -H W, -W W-G, V-H-W W-G, V-W such that W > G > H > 0. (Might make sense to also make restriction V > W + H but this is not mentioned in the definition of the game.)Generate a matrix a, w b, x c, y d, z such that either: a > c d > b x > w y > z or: c > a b > d w > x z > yDefine payoff for each player to be a constant times his For two players, generate a matrix: 0, -H W, -W W-G, V-H-W W-G, V-W such that W > G > H > 0. (Might make sense to also make restriction V > W + H but this is not mentioned in the definition of the game.)Generate a matrix a, w b, x c, y d, z such that either: a > c d > b x > w y > z or: c > a b > d w > x z > yDefine payoff for each player to be a constant times his own effort times the sum of the effortFor two players, generate a matrix: 0, -H W, -W W-G, V-H-W W-G, V-W such that W > G > H > 0. (Might make sense to also make restriction V > W + H but this is not mentioned in the definition of the game.)Generate a matrix a, w b, x c, y d, z such that either: a > c d > b x > w y > z or: c > a b > d w > x z > yDefine payoff for each player to be a constant times his own effort times the sum of the efforts of others all minus the cost of his own effort. Cost should be smooth, convex, and increasing. Need to think of best way to generate these functions, and also whether the problem would still be supermodular if we gave a fixed number of effort level choices to each player.W|qf[P|tDwL d|tDwL ګtDwL ګtDwL x-tDwL Աuuʫt DwL 0uu-tDwL eګtDwL 貦euthDwL  DuګtDwL  uu-tDwL  ueʫtTDwL  XE%Uʫt%TDwL  UeEeʫtDwL E%U-t TDwL l5t QDwL &ȵEU5UetPDwL $%%-tDwdL EUUګtDwL ܶe7t DwL 8-tDwL 7tDwL ګtDw貦L LE(tDwDL  (topDwL uuګte-DwlL `(tDwL eeee%(t`aDwL %%eګtDwL (tګt^8DwȵL &кeueeeeeګtpeDwL ,eeeeuueeګt0,DwL euuee-t`nDwL 仦eeeeeu5kt`gorDwL @ګtatDwL tDwL $tDwL DTueueeeee-t`DwL eeee%e{tp-DwL  eeeueuee-tDwL heeeue93_> <8 77 1 1 6-% K[M M̋ ʋʋʋʍNgame_game_subset_subform1game-game subset subform1o Actions_Extensible_Actions Extensible?o PlayPropData~ 15Ď(,`L-,Blob 9TypeInfo5  L !"#$%&'()*+,-./34678:;<=>?@ABCDEFGHIJKNOPQRSTUVWXYZ[\]^_`abcdeBlobDeltaDirData/fPropData3 1"@Jfmnoprz{mdmdmdjdodddjdmdpͬcNg.ID6A^FormHeaderDetailmnamed name_Labelmdescriptiond description_Labelmgenerated generate_Labeljcoding_completecoding completed coding_complete_Labelcoding complete_Labelo Combo10d Priority_Lanopdfddffmmmmname_LabelCategory Name&cateͬ_~!HJ)CPWPageHeaderSectionDetailPageFooterSectionReportHeaderReportFooterGroupHeader0mgame_namegame.namedgame_name_Labelgame.name_Labelmgame_1_namegame_1.named game_1_name_Labelgame_1.name_Labeld 4DcH fp)BlobDeltaTypeInfoBlobDeltaTypeInfo:9#BlobDelta PropData7 76_= 8f(Dͬ~ΩFoW썛PageHeaderSectionDetailPageFooterSectionReportHeaderReportFootermtitledtitle_Labelmauthorsdauthors_Labelm assignment_detailsassignment detailsd assignment_details_L LVALr1 } ^ ;  u ]   m P C 6 )   OO) ) ) )))pZero-Sum GamespWar of attrition6pUniform Local-Effect Game with clique-Uniform Local-Effect Game!pStag and Hare)Sm"Two animals are fighting over some prey. Each can behave like a dove or like a hawk. The best outcome for each animal is that in which it acts like a hawk while the other acts like a dove; the worst outcome is that in which both animals act like hawks. Each animal prefers to be hawkish if its opponent is dovish and dovish if its opponent is hawkish." With certain restrictions on the values of payoffs, this game can become Prisoner's Dilemma or Chicken. Has an evolutionarily stable strategy. 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Switch to another strategy with probability proportional to regret of not not playing it in the past. Converges to the set of epsilon-equilibria almost surely. No empirical results seem to be available, but should be very easy to implement.By Piero and Mark - do simulated annealing to find set of all NE's (in infitine time) of normal form games. Converges with probability 1, no timing guarantees, suggest that it's nice, because can be implemented as a decentralized adaptive procedure. Say not a bad heuristic.Polytime algorithm for finding NE in repeated bi-matrix games (Limit of the means payoff) Output is a FSA or a "counting node" representation (DFA with counting allowed?) Looks like a generalized tit-for-tat thing, with computation of "attack" and "defense" strategies. Computes tit-for-tat for prisonner's dilemma Equilibria computed are subgame perferct Mentions Unbalanced and Exponential games Cannot be generalized to finite-horizon or discounted payoffs, unless discount factor is set very close to 1 in a game-specific wayUses some sort of CSP formulation to find epsilon-nashA strict generalization of Lemke-Howson, follows path in Kohlberg-Mertens spaces to get to an equilibrium. Good experimental results.Iteratively finds a minimax solution. Algorithm is proved in this paper, but not explained.. Originally suggested in "Some Notes on Computation of Games Solutions" (Brown, 1949)For infinitely repeated games with perfect monitoring and public randomization. Computes Equilibrium actions and strategies. May not be useful to us at all.For infinitely repeated games with perfect monitoring and public randomization. Produces inner and outer approximations of the equilibrium value set. May not be useful to us at all.Each player best-responds to the fixed strategies of other agents. Convergence occurs when no agent wants to update his strategy, which by definition is a PSNE. There is no guantee of convergence. 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Walker (Ed.)@"h\\D   LVAL4 ` `` . ..n, did you write this one? I don't think this is the correct defGraphical game structured as a ring of rSum of players' payoffs is constantGraphical game structured as a ring of rings. Random(?) payoffs. Symmetric. I don't think this is actually symmetric --KRegular LEG with restriction that F_{a,a'} = F_{a,a''} for all a,a',a''. Equivalent to congestion game, and has PSNE.This game is described as a matrix. It cannot be scaled to different sizes.Games that can be represented more compactly than with a matrix"Supermodular games are games in which each plSum of players' payoffs is constantGraphical game structured as a ring of rings. Random(?) payoffs. Symmetric. Graphical game structured as a ring of rings. Random(?) payoffsGraphical game structured as a ring of rings. Random(?) payoffs. Symmetric. I don't think this is actually symmetric --KRegular LEG with restriction that F_{a,a'} = F_{a,a''} for all a,a',a''. Equivalent to congestion game, and has PSNE."Supermodular games are games in which each player's strategy set is partially ordered, the marginal returns to increasing one's strategy rise with increases in the cGraphical game structured as a ring of rings. Random(?) payoffs. Symmetric. I don't think this is actually symmetric --KRegular LEG with restriction that F_{a,a'} = F_{a,a''} for all a,a',a''. Equivalent to congestion game, and has PSNE."Each of two people chooses either Head or Tail. If the choices differ, person 1 pays person 2 a dollar; if they are the same, person 2 pays person 1 a dollar."Models a situation in which two players wish to coordinate their behavior, but have conflicting interests.- agents choose one node in a graph as their action - payoff function for choosing action a is: $$ F_{a,a}(D(a)) + \sum_{a' \in neigh(a)} F_{a',a}(D(a')) $$ - expresses context-specific independence between agent's utility functions.Local-effect game, with the restriction that F_{a,a'} = F_{a',a} for all {a,a'} Has property PSNE if all F are linear\LVALlNeeeee  ^  ǵ m 3 U | R | ||||||||||||||^ @ @@@@@@@@@@@@@@@@@@ 9 ȧk'''''''''' xVBAProjectNY`tYAcessVBAData   !0 "'#$%&(.)*+,-/41E235768<9:;=?>@ABCDVBAPY`tYPROJECTwmPROJECT_VBA_PROJECT /%ԫm@%ԫm@~sq_calgorithm-reference SuDPB_ ` 2? 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F-pF-HF-F-`F-referencePrimaryKeyF-`F-F-F-F-F-xF-pF-8F-pF-F-HF- LVALMR2 GUIDNameMap b8+mOvC]f ^ URAP)&\o@referenceV㛃H/ӯonRAP)&titlev2R{pI6#uRAP)&bibtexk&%^) LѳeŷRAP)&authorszEIJۮ RAP)&in queue9@N#_RAP)&comment1^'"3HD ERAP)&uselessSFK0s zRAP)&assigned toM#MF./ԅyk2Zo@XpeopletF,Kz1M#MF./ԅyname_QJe8r~UzM#MF./ԅyid^2 'J>'f\o@ 0algorithm-reference subform;ՊDO/ E n@)algorithm-reference@] բr@<4o ARAP)&id9bBgxWݘ՘@ 0game-reference subform2|C@a3-]n@game-referenceoNڽF5߾d|C@a3-referenceidLVAL  N & @article{Hotelling29, author={H. Hotelling}, title={Stability in Competition}, journal={Economic Journal}, volume={39}, pages={41--57}, year={1929}}@article{Rosenthal73, author={R.W. Rosenthal}, title={A Class of Games Possessing Pure-Strategy {Nash} Equilibria}, journal={International Journal of Game Theory}, volume={2}, pages={65--67}, year={1973}}@article{MondererShapley96, author={D. Monderer and L.S. Shapley}, title={Potential Games}, journal={Games and Economic Behavior}, volume={14}, pages={124--143}, year={1996}}@techreport{ConitzerSandholm, AUTHOR = "V. Conitzer and T. Sandholm", TITLE = "{Complexity Results about Nash Equilibria}", INSTITUTION = "{CMU}", YEAR = 2002, NUMBER = "CM-CS-02-135" }@inproceedings{HuWellman, author={J. Hu and M.P. Wellman}, title={Multi-Agent Reinforcement Learning: Theoretical Framework and an Algorithm}, booktitle={ICML}, year=1998 }@article{Nash50, AUTHOR= "J.F. Nash", TITLE = "Equilibrium Points in N-Person Games", JOURNAL = "Proceedings of the National Academy of Sciences of the United States of America", YEAR = 1950, VOLUME = 36, PAGES = "48--49" }@misc{ johansson-game, author = "Stefan J. Johansson", title = "Game Theory and Agents", url = "citeseer.nj.nec.com/johansson99game.html" }@inproceedings{ yao94experimental, author = "Xin Yao and Paul J. Darwen", title = "An Experimental Study of N-Person Iterated Prisoner's Dilemma Games", booktitle = "Evo Workshops", pages = "90-108", year = "1994", url = "citeseer.nj.nec.com/yao94experimental.html" }@book{OsbRub, AUTHOR = "M.J. Osborne and A. Rubinstein", TITLE = "A Course in Game Theory", PUBLISHER = "MIT Press", YEAR = 1994 }@inproceedings{LEG, title = "Local-Effect Games", author = "K. Leyton-Brown and M. 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ȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȤȑ}jjjjjjjjjjjjjjjjjjjjjjjjjjjjjd 9 d 9 c 8 c ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{d 9 d 9 d 9 c 8 c ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{d 9 d 9 a 8 a 8 a ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>a 8 a 8 a 8 a ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>a 8 a 8 a 8 a ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>a 8 a 8 a 8 a ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>a 8 a 8 a 8 a ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>a 8 a 8 a 8 a ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>a 8 [ 8 [ 8 [ ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>[ 8 Z 8 Z ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up Z 9 Y 8 Y ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up Y 9 S8 S;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up S9 28 2;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up 29 N 8 N ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up N 9 M 8 M ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up M 9 L 8 L ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up L 9 K 8 K ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up K 9 J9 J;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up J8 I8 I;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up I9 H9 H;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up H8 G8 G;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up G9 F 8 F ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up F 9 E9 E;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up E8 m+}N((reference.title="Algorithms for Games"))reference.[assign :The Complexity of two-person zero-sum games in extensive form.D. Koller, N. Meggido@"maaJ  LVALMR2 GUIDNameMap  qi N:S  URAP)&\o@referenceV㛃H/ӯonRAP)&Titlev2R{pI6#uRAP)&Bibtexk&%^) LѳeŷRAP)&Authors^2 'J>'f\o@P 0algorithm-reference subform;ՊDO/ E n@ algorithm-reference@] բr@<4o ARAP)&id9bBgxWݘ՘@ 0game-reference subform2|C@a3-]n@ game-referenceoNڽF5߾d|C@a3-referenceid vcccccccccccccccccccccccccccccccccccccP<)))))))))))))))))))))))))))))))))))))))))))))) y  e R RRRRRRRRR? ˵˵˵˵˵˵˵˵˵˵˵ˢ +   !"#$%&'()*+,-./0123I8I9I:-}P-}Q-}R.}S.}T.}U/}h/}i/}j3}z3}{3}|7}7}7}<}<}<}=}=}=}>}>}> 8  8  ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ> 8  8  8  ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ> 8  8  8  ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ> 8  8  ;$ o`zzi ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up  8  8  ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ> 8  8  8  ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ> 8  8  8  ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ> 8  8  8  ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ> 8  8  8  ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ> 8  8  8  ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ> 8  8  8  ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ> 8  8  8  ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ> 8 9 ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up 8 8 ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up 9 8 ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up 9  8  ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up  9 9 ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up 8  8  ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up  9 9 ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up 8  8  ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up  9 -LVAL=LhH X @  h0Xhh LVAL "A geometric game is a game having the following form: Two antagonists, known hereafter as RED and BLUE, choose subsets R and B respectively of a set S. BLUE then receives from RED a payoff which is a function of the triple R, B, and R (intersection) B. The payoff need not be monetary, and for our purposes can be considered merely a score which BLUE wishes to maximize and RED wishes to minimize. . . . In general, RED and BLUE may not choose any subset of S, but rather RED must select from a collection R of admissible pure strategies for RED and BLUE from a collection B. . . . The term 'geometric' is described by specifying S, R, B, and the payoff.""At each play, Ruth and Charlie simultaneously extend either one finger or two fingers and call out a number. The player whose call equals the total number of extended fingers wins that many pennies from the opponent. In the event that neither players' call matches the total, no money changes hands." Four by four matrix of choices for each player. In the finger story, choose a pair of numbers representing the number of fingers you hold out and the number of fingers you think there will be total. Choices are (1, 2), (1, 3), (2, 3), and (2, 4)No description given except for payoff matrix. Looks rather uninteresting since both players have dominant strategies which lead them both to their highest payoffs.This version of the problem is from Rationalizability. . but is based on an earlier version of the problem, also proposed by Milgrom and Roberts. A team of managers run a firm and adapt to changing technology. They all share a common payoff function f which is also the payoff of the firm and also a supermodular function. The details as given in this paper are fuzzy. 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Local-Effect Games@@Local-Effect GamesTT@4((?erPrisoner's Dilemmah@b@Prisoner's DilemmaTT@4((_LVAL#hD >  `? >>>p>  >>>>>>>>  =algorithm-reference.algorithmid%algorithm-reference=algorithm-reference.referenceidp>h>> > (> S+n@(>P>pD>p$7>p$algorithm-reference0>>> >(>E n@A~sq_falgorithm-reference Subform1P> >> >>>> >p$7>p$algorithm-reference >> >>>> >> > (>8>@>H>P>X>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>x>>H > > > > > >z  >> >$P>p > > >p > >0x > >p > > >%algorithm-reference >8 >x > > >referenceid7referencealgorithm-referencePrimaryKeyalgorithmid7algorithmalgorithm-reference >>v  >>>>>q>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>h>>-p>algorithm-referencePrimaryKey>p> > > >>>>X>>> > LVAL N>> DDDDDDDD @@`@ @  @ @`@@@Similar to 2x2 version of prisoner's dilemma but extended to n players and n actions. "More aptly considered as games of chicken." - Game Theory Topics "Game Theory and Experimental Games" makes reference to three independent discoveries of this game in 1973: Schelling, Hamburger, and Dawes It also speaks of three situations which can be modeled as N-Player Prisoner's Dilemma games: - the invisible hand (page 157) - conservation of scarce resources (158) - the tragedy of the commons (159) LVALD(F(T p?@ F(FF F4  FFFFFFFF d  people.name peoplepeople.idFFFF Fhjr@FF YE EFh YEEFh YEEpeopleFXFxF8 FFk2Zo@3~sq_creference~sq_cCombo30F FHF FPFFF FhFhpeople FF FFFF F Fp F F8F@FHFPFXFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFxF8F F F8 F hF8 F`Fz  FF FHkF F FP F d F F0 F F F F8 F people F8 FPrimaryKeyidH FFv `F8FHFF F Fq F F F F F F F F F F F F F F F F F F F F F F F F F F F FFFFF F FpeoplePrimaryKeyhF F`F` F`FhF FFFFF8 F LVAL s`# ) e %  uThe Strategy of Conflict _Team GIntroduces a new notion of equilibrium "Quantal Response" Idea is that players have a probability distribution over strategies (due to them making errors), better strategies have higher mass, and there are some constraints. They show existence, and stuff, and consider a specific family for errors logit. Then they fit that to experimental data, and apparently find correlations. More relevant to experimental stuff, games don't seem to be particularly interesting. Claim that it has some sort of learning built in.LVAL$http://www.chass.utoronto.ca/~osborne/2x3/tutorial/index.htmlhttp://cowles.econ.yale.edu/P/cd/d12b/d1275-r.pdf LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLReplicable  <     &  U'ςO>;{8L)x@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byL~Jޘ)9g'ςO>;{included ^2”eIG`<}sLVALT T* 44{tmf_XQJC<5.'  xqjc\UNG@92+$Journal of Peace Science 2, p 171-203. Green JX1901 .J63 V.2-4 found on http://www.economics.laurentian.ca/strategic_think.27/modules/course_schedule.98/2x2%20games/typology_of_%202x2.htmDefines the class of dispersion games, and demonstrates reinforcement-learning convergence results based on the amount of information agents have about each others' action choices.If timeDefines the class of dispersion games, and demonstrates reinforcement-learning convergence results based on the amount of information agents have about each others' action choices.If time permits, there are a lot of games mentioned in the exercises at the end of some of the chapters that might be worth thinking about, although I would imagine most of them are fairly arbitrary.This presents a generalized sort of Turing machine (called "probabilistic game automaton") that acts as a computational model of 2-player zero-sum interaction. Basically, both players are able to control the transitions of the machine, rather than just one as in a TM. There is some facility made for random moves, keeping moves secret from the other player, and bounded time or space for making a move.http://sobek.colorado.edu/~mciverj/4224_res.html Lists 2x2 games as classified in the Rapoport book.. Class I - Each player has a dominant strategy Class II - One player has a dominant strategy Class III - No player has a dominant strategy also gives examples of games with various liabilities (no liability, strict liability, etc)SvЩ w E E K Kˈ ʈʈʈʈʈʈʟ ƴƴƴƴƴIEFf22222Mc`z!uu@`z!uu@~sq_fgenerator coding queunΔu@Δu@~sq_cGenerators~sq_cgame-game subset subform19 @4MR2KeepLocal T||||||z `Y"pu@"pu@~sq_cSets of Games~sq_cgame-reference subform19~ @v4MR2KeepLocal T~~~~~~| `N jr@;jr@~sq_freference9$@4MR2KeepLocal TJ>>>>>>< `M6>>>>>>< @IN0wp@o@Superset Query9(V@@bVVJ>>>>>>< `HTvp@Tvp@Subset Query9@c FFF:::::::8 @Gvp@VU@Subset Query9[@m @^RRF::::::8 `F`vp@Zvp@~sq_rgame-game subset96@4MR2KeepLocal TXLLLLLLJ `EZo@EZo@Sets of Games9@3HHH<<<<<<<: @g|Yo@S|-x@Generators9GMV@E|@ZNNB6666664 `#n@#n@Unassigned References9b@OXXXLLLLLLLJ @QÏn@gn@Unassigned References9@@7|@NpddXLLLLLLJ `Fn@#讶@reference Query9@u |@XLL@@@@@@@> @saϗn@saϗn@~sq_rAll References In List9x @P4MR2KeepLocal TdXXXXXXV `C^ϗn@C^ϗn@All References In List9v@ZZZNNNNNNNL @:,?n@-?n@~sq_cgame-reference subform~sq_creferenceid9( @4MR2KeepLocal Txxxxxxv `In@In@peoplereference9@@@@@@@@@@> %Jn@%Jn@References Assigned to Kevin9p@IfffZZZZZZZX @un@un@References Assigned to Alex9n@dddXXXXXXXV @ LVAL, "Let L be a set containing n points, R the collection of all subsets of L containing at most p points, and B the collection of all subsets of L containing at most q points. RED chooses a member of R; BLUE chooses a member of B." The payoff to BLUE (from RED) is 1 if the intersection of these chosen sets is empty and 0 otherwise. RED should always choose the largest set possible and BLUE should always choose the smallest set. Example scenario: Surveillance. "A suspect will transfer envelopes to six different contacts during the cour se of a day. Two of these envelopes contain industrial secrets and the rest contain legitimate information. Three investigators are available to observe the contacts. Each investigator can monitor one contact. One observed exchange of industrial secrets will suffice to convict the subject." Here n = 6, q = 2, p = 3. LVAL MR2 GUIDNameMap  qi N:S  URAP)&-e򣶞@referenceV㛃H/ӯonRAP)&Titlev2R{pI6#uRAP)&Bibtexk&%^) LѳeŷRAP)&Authors^2 'J>'f\o@P 0algorithm-reference subform;ՊDO/ E n@algorithm-reference@] բr@<4o ARAP)&id9bBgxWݘ՘@ 0game-reference subform2|C@a3-]n@game-referenceoNڽF5߾d|C@a3-referenceid LΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞΞ΀bD ͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔͔x pe  pe  pe reference.title. pe reference.title. ' pe reference.title. ' pe reference.title. ' pe reference.title. 'e  pe reference.title. ' pe reference.title. ' pe reference.title. 'referenreference### reference##reference###  reference### reference###  reference###   reference###   Greferenreferenreference### reference###  reference###  reference###  reference###   reference###   Greferenreferenreference##referenreference###   reference###  referenreferenreference##referenreference###   Greference###  referenreferenreference##referenreference###   Greference###  referenreferenreference##referenreference###   Greference###  referenreferenreferenreference###  . reference###    . reference###   . reference###. reference###  . reference###    G.    Ggame   G  GRBOgame-reference--- RBOgame BOgamegame-referenceF@HoA5 BO[game-reference].gameid6 gBO game.name( gRBO BO GPLVAL x xxxxx ʬ | k *  tGames which have three equilibria: - two asymmetric equilibria in pure strategies - one symmetrNo description given except payoff matrix. Looks like point is that both players have dominant strategies and converge on their second highest payoffs.Games which have three equilibria: - two asymmetric equilibria in pure strategies - one symmetric equilibrium in mixed strategyGames in which no players have dominant strategiesGames in which all players have dominant strategiesThe interests of players partially coincide in that it is possible both may prefer one outcome to another.Games in which the gains of each player as he shiftNo description given except payoff matrix. Looks like point is that both players have dominant strategies and converge on their second highest payoffs.GamNo description given except payoff matrix. Looks like point is that both players have dominant strategies and converge on their second highest payoffsNo description given except payoff matrix. Looks like point is that both players have dominant strategiesNo description given except payoff matrix. Looks like point is that both players have dominant strategies and converge on their second highest payoffs.Games which have three equilibria: - two asymmetric equilibria in pure strategies - one symmetric equilibrium in mixed strategyGames in which no players have dominant strategiesGames in which all players have dominant strategiesA graphical game - players along a road, interact with N,E,S,W neighbours only. Payoffs arbitrary - usually Roshambo style. Have also some economically motivated payoff-structure in Koller/vickreyGames resulting from Conitzer/Sandholm SAT reduction. Games that come from SAT formulae using their reduction! (Might be an idea for a weird continuation-method-based SAT solver). Symmetric, two-player. Has only symmetric equilibria, with each supported action having equal probability, and one default pure-strategy equilibrium. Interesting to find non-default equilibria only. +  @@@ @@@Md`fomYbUkofQiUJ`QQhoY^YLiYJuMdbUQkmYdbUJ`QkJbOfdmQbmYJ^kiQMdbkYOQiQOB OQMQfmYdbYb:u:UJ`QkBOYSSQiQbmYJ^UJ`Qku%OYkfQikYdbUJ`QkBOd`YbJbMQkd^qJL^QQbU^YkW`o^mYYmQ`JoMmYdbkBOvbJ`YMUJ`QkdSYbbdqJmYdbuOvbJ`YMbdbMddfQiJmYqQUJ`QmWQdivQSSYMYQbmMd`fomJmYdbdSLQWJqYdikmiJmQUYQkBQSSYMYQbmMd`fomJmYdbdSQhoY^YLiYJSdiQumQbkYqQmsdfQikdbUJ`Qk_QSSYMYQbmbJkWMd`fomJmYdbYb^JiUQfdfo^JmYdbUJ`QksYmWLdobOQOYbS^oQbMQ_ QhoY^YLiYo`YYY kd`QiQMQbmmvfQkdSQhoY^YLiYo``dOQ^kQhoY^YLiYo`YbWdmQ^^YbUk`dOQ^dSkfJmYJ^Md`fQmYmYdbg_QhoY^YLiYo`fdYbmkYbbdbxQidko`bfQikdbkofQi`dOo^JiUJ`Qk{uQhoY^YLiYo`fdYbmkYbbfQikdbUJ`Qkcu Qqd^omYdbJivUJ`QmWQdivBQuYkmQbMQdSbJkWQhoY^YLiYo`YbbfQikdbUJ`QksYmWdomhoJkYMdbMJqYmvu!QudmYMfWQbd`QbJYbUJ`QkJbOOodfd^v`dOQ^ku SiYQbOdiSdQh^QJibYbUYbUQbQiJ^ko`UJ`Qk';BUJ`QmWQdivYu UJ`QmWQdivYYu UJ`QmWQdivJbOJUQbmkuUJ`QmWQdivJbOQufQiY`QbmJ^UJ`QkB UJ`QmWQdivJkJmWQdivdSMdbS^YMmiQkd^omYdb_UJ`QmWQdivmdfYMk YbMd`f^QmQYbSdi`JmYdbiQfQJmQOUJ`QkJbObf^JvQiUJ`Qk _ UJ`QkJbOOQMYkYdbkuUJ`QkJbOYbSdi`JmYdbb^JiUQfdfo^JmYdbUJ`QksYmWLdobOQOYbS^oQbMQ_ QhoY^YLiYo`YYY kd`QiQMQbmmvfQkdSQhoY^YLiYo``dOQ^kQhoY^YLiYo`YbWdmQ^^YbUk`dOQ^dSMd`fQmYmYdbg_QhoY^YLiYo`fdYbmkYbbdbxQidko`bfQikdbkofQi`dOo^JiUJ`Qk{uQhoY^YLiYo`fdYbmkYbbfQikdbUJ`Qkcu QuYkmQbMQdSbJkWQhoY^YLiYo`YbbfQikdbUJ`QksYmWdomhoJkYMdbMJqYmvu!QudmYMfWQbd`QbJYbUJ`QkJbOOodfd^v`dOQ^ku UJ`QmWQdivYu UJ`QmWQdivYYu UJ`QmWQdivJbOJUQbmkuUJ`QmWQdivJkJmWQdivdSMdbS^YMmiQkd^omYdb_UJ`QmWQdivmdfYMk YbMd`f^QmQYbSdi`JmYdbiQfQJmQOUJ`QkJbObf^JvQiUJ`Qk _ UJ`QkJbOOQMYkYdbkuUJ`QkJbOYbSdi`JmYdb_ UJ`QkJbOOQMYkYdbkuUJ`QkJbOYbSdi`JmYdbu`dOQ^kdSkmiJmQUYMiJmYdbJ^Ymv_`dbdmdbQMd`fJiJmYqQkmJmYMku`o^mYJUQbmJ^UdiYmW`kSdikd^qYbUUiJfWYMJ^UJ`Qk_`o^mYJUQbmYbS^oQbMQOYJUiJ`kSdiiQfiQkQbmYbUJbOkd^qYbUUJ`Qk_`o^mYJUQbmiQYbSdiMQ`Qbm^QJibYbU mWQdiQmYMJ^SiJ`Qsdi\JbOJbJ^UdiYmW`_bJkWQhoY^YLiYo`Ybd^YUdfd^vUJ`QksYmW`dbdmdbQLQkmiQkfdbkQkubJkWQhoY^YLiYo`sYmWkmiJmQUYMMd`f^Q`QbmJiYmYQkubJkWfidfJUJmYdbSdi^ddfvUiJfWYMJ^UJ`Qk_dbmWQbfMd`f^QmQbQkkdSSYbOYbUJbdfmY`J^kmiJmQUvYbUJ`QksYmWMd``dbfJvdSSk+_fOSMdiQQhoYqJ^QbMQmWQdiQ`kSdiYbSYbYmQMdbqQuUJ`Qk_fdmQbmYJ^UJ`Qk_foiQbJkWQhoY^YLiYJ WJiOJbOQJkvUJ`Qku iJmYdbJ^YxJLY^Ymv^QJibYbUJbOQhoY^YLiYo`YbUJ`QksYmWkmiJmQUYMMd`f^Q`QbmJiYmYQkukQ^QMmYdbMiYmQiYJYbMddiOYbJmYdbUJ`Qk kd`QQufQiY`QbmJ^iQko^mkukY`o^JmQOJbbQJ^YbUdSUJ`QkQhoY^YLiYJ_kd`QmdfYMkYbmsdfQikdbUJ`QkOu$kmJLY^YmvYbMd`fQmYmYdb_koL[QMmYqQiQJkdbYbUYbOvbJ`YMUJ`Qk_koSSYMYQbMvMdbOYmYdbkSdibJkWQhoY^YLiYo`YbbfQikdbOYSSQiQbmYJ^UJ`Qku&mQJ`UJ`QkJk`dOQ^kdSYbmQiUidofMdbS^YMmk_mWQMd`f^QuYmvdSmsdfQikdbxQidko`UJ`QkYbQumQbkYqQSdi`[_mWQkQmdSbJkWQhoY^YLiYJdSJkofQi`dOo^JiUJ`QYkJMd`f^QmQ^JmmYMQumWQkmiJmQUvdSMdbS^YMmumWQdivdSUJ`QkJbOQMdbd`YMLQWJqYdiqJ^oQkdSk`ddmWbdbJmd`YMUJ`Qk mWQ`QmWdOdS`o^mY^YbQJiJffiduY`JmYdbYbmWQkWJf^QvqJ^oQW_sQLfJUQ8_sQYUWmQO`J[diYmvUJ`QkWJqQ`Jbv`oqJ^oQk_ # LVAL {M ~Y1  p V : ' m J 6  p L 4 o [ ?  k ^ UU ))pZero-Sum Games )Welfare GamepWar of attrition6pUniform Local-Effect Game with clique-Uniform Local-Effect Game!)Travellers DilemmapStag and Hare)Spite )Small Pig)Simplified Poker)Simple PoiSymmetric 2x2 games extended to N+1 (by this notation..) players. Assume the original 2x2 game had choices we will call C (cooperate) and D (defect) and was of the form R, R S, T T, S P, P with no restrictions on the values of P, R, S, and T. For any player let N be the number of other players in the game, and x be the number of other players who cooperate. Then the payoff function for this player is as follows: P(C) = Rx + S(N-x) P(D) = Tx + P(N-x) T > S > R > P is multi-person Leader S > T > R > P is multi-person Battle of the Sexes T > R > S > P is multi-person Chicken R > T > P > S is multi-person maximizing difference game\i-y< > ̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̿̊ S G  ʩʩʩʩʩʩʩʩʩʩʩʩʩʩʩʩʩʩʩʩʩʩʩʋ m O h h   G!  G      G!  G      G!([_  G      Gri Gri GOri!ri GOri!ri GOri!ri GOri!ri Gri Gri Gri GOri!ri GOri!ri GOri!([__ri GOri!ri Gri Gri Gri GOri!ri GOri!ri GOri!([__ri GOri!ri Gri GOri!([__algorithmid] = algorithmid)> 'ri__algorithmid+++ OOrialgorithm-referenceGAMUT AlgorithmsWW7  ri GOri ri GI  game_1.name* 'I  game.name( 'Igamegame_1%% Igame-game subset111 Igame Igamegame-game subsetL@oE9 Igame-game subsetgame_1R@oI=1 I game_1.name* gI game.name( gOri (((game.[is generator])=True))= ' Ori game.name( 'ri game.[coding complete]5 gri game.included, grigame.[extensible-player]7 grigame.[is generator]2 grigame.[entered by]0 gri game.gameid* grigame.generate, grigame.[extensible-action]7 grigame.description/ gri game.name( gOrigame ri Gri G LVAL Naā B BBB˵ ʵʵʵ@ @@@@@@@@@@@@@@@@ d ddddddddddddddɯ4R#B @ @ @ @ @ @ $v$o$p$q$r$s$t$u Rvr@vr@~sq_cGenerators~sq_cText1894MR2KeepLocal TVVVVVVVT @QOvr@vr@~sq_cGenerators~sq_cgame-reference subform19y @4MR2KeepLocal Txxxxxxv `PTur@Ovr@~sq_cGenerators~sq_cgame-game subset subform9 @4MR2KeepLocal Tzzzzzzx `O tr@ur@~sq_cGenerators~sq_cgame-game subset subform19x @4MR2KeepLocal T||||||z `JG=wp@G=wp@Superset Query9@E}JJJ>>>>>>>< @IN0wp@_L=wp@Superset Query9?v@J}@bVVJ>>>>>>< `HTvp@Tvp@Subset Query9@.}FFF:::::::8 @Gvp@T wp@Subset Query9W;v@:@^RRF::::::8 `F`vp@Zvp@~sq_rgame-game subset96@4MR2KeepLocal TXLLLLLLJ `EZo@EZo@Sets of Games9@ HHH<<<<<<<: @g|Yo@l˹Xp@Generators9@`@"l|@ZNNB6666664 `#n@#n@Unassigned References9b@ XXXLLLLLLLJ @QÏn@gn@Unassigned References9-@A@K}|@NpddXLLLLLLJ `Fn@PFn@reference Query9{@@ |@ NdXXL@@@@@@> `saϗn@saϗn@~sq_rAll References In List9x @P4MR2KeepLocal TdXXXXXXV `C^ϗn@C^ϗn@All References In List9v@VOZLooks very similar to Battle of the Sexes except with different payoffs in the two least preferred squares. A "hero" is "one who acts to benefit others as well as himself, but others more than himself" which is the case for either player switching from the (c, c) outsome to (a, b) or (b, a). Both players would rather the other switched, but would rather switch themselves than stay at (c, c). LVALMR2 GUIDNameMap.  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RED chooses a member of R; BLUE chooses a member of B." The payoff to BLUE is 1 if the intersection of these chosen sets is empty and 0 otherwise. RED should always choose the largest set possible and BLUE should always choose the smallest set."A geometric game is a game having the following form: Two antagonists, known hereafter as RED and BLUE, choose subsets R and B respectively of a set S. BLUE then receives from RED a payoff which is a function of the triple R, B, and R (intersection) B. The payoff need not be monetary, and for our purposes can be considered merely a score which BLUE wishes to maximize and RED wishes to minimize. . . . In general, RED and BLUE may not choose any subset of S, but rather RED must select from a collection R of admissible pure strategies for RED and BLUE from a collection B. . . . The term 'geometric' is described by specifying S, R, B, and the payoff."This book gives a lot of descriptions of ways that you can have a simplified poker game where each of the two players only draws one card which is either high or low. Most of these versions cannot be represented in normal form because there is a nature player involved in determining which of the two has the high card and which has low. This version is an averaged version of some of the others. Player 1 has 8 pure strategies which are each combinations of the strategies bet, pass and fold if the other player bets, pass and call if the other player bets. Player 2 has 4 pure strategies which are combinations of folding, betting, and calling.LVAL ʼʼʼʼʼJ1  s ` B !  d 7  @ (  } b Generate payoff matrix b, b c, c d, c a, a such that a > b > c and a, b, and c are very signicantly larger than d. For example: 1, 1 -1, -1 -1000, -1 Generate payoff matrix b, b c, c d, c a, a such that a > b > c and a, b, and c are very signicantly larger than d. For example: 1, 1 -1, -1 -1000, -1 2, 2 Could extend but may not be as interesting anymore.Parametrize on n, p, and q. There will be (n choose p) + (n choose p-1) + . . . + (n choose 1) choices for RED and (n choose q) + (n choose q-1) + . . . + (n choose 1) choices for BLUE, so the matrix will blow up pretty fast.Just like simple inspection game except set payoffs differently.. Parametrize on n, p, and q. There will be (n choose p) + (n choose p-1) + . . . + (n choose 1) choices for RED and (n choose q) + (n choose q-1) + . . . + (n choose 1) choices for BLUE, so the matrix will blow up pretty fast.Similar to simple inspection game except set payoffs differently.. Parametrize on n and p. There will be (n choose p) +( n choose p-1) + . . . + (n choose 1) choices for RED and (n choose n) + (n choose n-1) + . . . + (n choose 1) choices for BLUE, so the matrix will blow up pretty fast . . .Generate a payoff matrix with 8 choices for player 1 and 4 for player 2. Since this matrix is zero-sum, I will only list the payoffs for player 1 here .. Subtract these from 0 to get the payoffs for player 2: a a 0 0 a/2 0 b/2 (b-a)/2 a/2 (a-b)/2 b/2 0 a/2 0 -b/2 (-a-b)/2 0 -a 0 -a 0 (-a-b)/2 0 (-a-b)/2 a/2 (a+b)/2 -b/2 0 0 (b-a)/2 0 (b-a)/2 0 0 0 0+{tmf_XQJC<5.'  xqjc\UNG@92+$  B B B B BBBBBBBBB __________________ _ _ _ _ _________&u%u$u#u"u!u uuuuuuuuu ZA Gentle Introduction to Game TheorySaul Stahl@H<<0  " LVAL 8 8B Generate payoff matrix a, a c, a a, c b, b where a > b > c Instead of creating a separate generator for this, it might be good to add a parameter to Prisoner's Dilemma for whether or not to allow this with some probability.Generate a payoff matrix a, w b, x c, y d, z such thGenerate payoff matrix a, a c, a a, c b, b where a > b > c Instead of creating a separate generator for this, it might be good to Generate payoff matrix a, a c, a a, c b, b where a > b > c Instead of creating a separate generator for this, it might be good to add a parameter to Prisoner's Dilemma for whether or not to allow this Generate payoff matrix a, a c, a a, c b, b where a > b > c Instead of creating a separate generator for this, it might be good to add a parameter to Prisoner's Dilemma for whether or not to allow thGenerate payoff matrix a, a c, a a, c b, b where a > b > c Instead of creating a separate generator for this, it might be good to add a parameter to Prisoner's Dilemma Generate payoff matrix a, a c, a a, c b, b where a > b > c Instead of creating a separate generator for this, it might be good to add a parameter to Prisoner's Dilemma for whether or not to allow this with some probability.Generate a range of discrete dollar amounts that the players can choose to claim. Payoff is the minimum amount claimed by any player, plus a small amount for the player with the lowest claim, possibly minus a small amount for other players.Generate values for a, b, and c (values used in the paper are a = 60, b = 20, c = 10) such that b > c. Generate random number of effort levels n and let each player have choices 1, 2, ..., n. Calculate payoff function using a + bM - cE.F@@Potential Games==, N@5|qf[PE:/$ti^SH=2' ͣ w l a V K @ 5 *   z o d Y N C 8 - "   ˓ } r g \ Q F ; 0 %    ʋ u j _T I > 3 (    x m b W L A 6+  {peZOD9.# ~sh]RG<1&???????game gamegame-referenceF@CoA5 [game-reference].gameid6 g game.name( g  GB([__id] = referenceid)5 '__id OBgame-referencereference??-   GB /////poocog.nn1f3fmM]]]]fjiiihIh/hh?hhY~f|g gag2fSfz y x w v u t s r oepcpdUc coco+o^mbnamal0k7k>3NVNANBN5N"N>Ne<d<S\c\ \\C\\*\Y\G\0\`]_Y^Y]Y\Y YSZZZCZ[ZZYYZ/Z0Z ZUZW?V?C?U??SR+Q(Q#Q$QPLRMQMQLLPLFLNL LCLMLLLLJLILHLLFODJCJ JMBMAM@M"M'6'3'1= < ; : 9 8.8-8 8 3 0 /./-/ / -M,6+M*M(M&M%6%-% $M#M" 1,66.-                 LVALD(4 (T p?@ 4(44 44  44444444 d  people.name peoplepeople.id4444 4Δu@44 4w 4wpeople4X4x48 44k2Zo@3~sq_cGenerators~sq_cText184 4H4 4P4444w 4wpeople 44 4444 4 4p 4 484@4H4P4X4444444444444444444444444444444444444444444444444444444444444x484 4 48 4 h48 4`4z  44 4w4 4 4P 4 d 4 40 4 4 4 48 4 people 48 4PrimaryKeyidH 44ev `484H44 4 q4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44444 4 4peoplePrimaryKeyh4 4`4` 4`4h4 444448 4LVALhD XVH XT ?hVXVVVn AVVDVtVVV0V`VVVVVVVDVtV      algorithm.namealgorithm)algorithm.description)algorithm.algorithmid'algorithm.entered byVV`VV Vk@VVV%qUCV% UDV% UtV% UalgorithmVVV VVk2Zo@)~sq_fGAMUT AlgorithmsV VVVV 0VV `VVVV0V`V V%CV%DV%ptV%Halgorithm VV VV DVV tVVVV0V`V VVV V8VHVXVhVxVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVhV`VHV V V V $V V`V V Vz VVVؐ%V V  V V@ V Vx V V  V  V@ Vx V8VVVV V V@ Vx V ValgorithmV0VPVPrimaryKeypeoplealgorithmalgorithmidpVVv V`VxVVVqVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV VVVPVValgorithmPrimaryKeyVVV VVVVVVV8V V ϦψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψψjLa _ 5  Q ii([__id] reference.authorsreference.authors0 reference.authors0 greference.authors0 greference.authors0 greference.authors0 greference.areference.authors0 reference.authorsreference.authors0 greference.authors0 reference.authors0 greference.authors0 greference.authors0 grefereferenreference.authors0 greference.authors0 greferenreference.authors0 greference.authors0 greference.authorsreference.authors0 reference.authors0 greference.areference.authors0reference.authors0reference.authorsreference.authors0 reference.authors0 greference.authors0 greference.authors0 greference.authors0 greference.authors0 greference.authors0 greference.authors0 greference.authors0 reference.authors0 greference.title. greference###  G G@`o ' reference.title. 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Let L be a set containing n points, R the collection of all subsets of L containing at most p points, and B the collection of all subsets of L. RED chooses a member of R; BLUE chooses a member of B. If the intersection of the chosen sets is empty, the payoffs are 0. Otherwise, the payoff to BLUE (from RED) is the size of the set chosen by BLUE."Let L be a set containing n points, R tAgain, very similar to inspection game. Let L be a set containing n points, R the collection of all subsets of L containing at most p points, and B the collection of all subsets of L. RED chooses a member of R; BLUE chooses a member of B. If the intersection of the chosen sets is empty, the payoffs are 0. Otherwise, the payoff to BLUE (from RED) is the size of the set chosen by BLUE.Exactly like Simple Inspection Game except with different payoffs. Let L be a set containing n points, R the collection of all subsets of L containing at most p points, and B the collection of all subsets of L containing at most q points. RED chooses a member of R; BLUE chooses a member of B. 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OpenChildForm-ToggleLink_Click_ExitEn NewRecordFormsproperty-reference DataEntryFilter;FilterOn&DoCmdƧOpenFormacFormSysCmdGacSysCmdGetObjectState?acObjStateOpen>Form_referenceCurrenteClick _B_str_ErrorR referenceid, propertyidPpropertyid_Labeln Form_Load{ Form_Load_ErrXpP ";"reference";"";"id";"title";"PrimaryKey"d5U`<axbc"referenceid_LabelReferenced in}7aeD'KM`FormFooteruǖOuռd:tegoryidJennTimes New Roman:0D1A`"PageHeaderSectiony'3LP8fz`4 DetailYNB㠽m5F`a<b\c, title ( LVALЈ A game over a network, each agent wants to send something from a fixed source to a fixed destination. Interesting question to ask: the ratio between worst NE and the social optimum. Examples of latency functions (from roughgarden): polynomials of degree <= p M/M/1: (u-x)^(-1) M/G/1: 1/u + (x (1+s^2u^2))/(2u(u-x))Graph consists of m parallel links from source to destination, all with same capacity. (So m = #actions) Equivalent to scheduling of some sort. See paper for a more precise descripA game over a network, each agent wants to send something from a fixed source to a fixed destination. Interesting question to ask: the ratio between worst NE and the social optimum. Examples of latency functions (from roughgarden): polynomials of degree <= p M/M/1: (u-x)^(-1) M/G/1: 1/u + (x (1+s^2u^2))/(2u(u-x))Graph consists of m parallel links from source to destination, all with same capacity. (So m = #actions) Equivalent to scheduling of some sort. See paper for a more precise description. LVAL CCCC CCEquivalent to potential games --- In congestion games, each player picks a subset of available facilities. For each facility the player chooses, he receives a payment based only on the number of players choosing the facility. The payoff for each player is the sum of these payments over all chosen facilities. Most definitions of congestion games involve (directly or indirectly) four properties (outlined by Voorneveld et al): P1) exists a finite facilty set P2) "Independence of irrevelant choices" P3) "anonymity" (although not necessarily symmetry, players can have different utility functions from each other) P4) "partial rivalry", i.e. you will never hurt from having someone who has chosen the same facility as you choose something else LVALNAAMR2ANSI Query ModeAccessVersion BuildProjVerHasCustomGroupsAppTitleStartUpForm&StartUpShowDBWindow(StartUpShowStatusBarStartUpMenuBar$AllowShortcutMenusAllowFullMenus(AllowBuiltInToolbars&AllowToolbarChanges AllowSpecialKeysAppIcon,StartupShortcutMenuBar&UseAppIconForFrmRpt.Use Default Page Folder0HaveSetDefaultPageFolder   08.50                 LVALrrϢNDoes loopy message passing on graphical gamesDoes loopy message passing on graphical games. Seems to find epsilon-equlibria. Doesn't always converge.Solves tree-structure graphical games via message passing of some sort. & @ @ @ @ @.h.h.h.h/h/h/h/h/h7377757674?N?P?Q?Obbbbj(j,j*j+j-j)k.k0k1k/nQnSnTnRnRnRnRnRnRnRnRnRxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxyyyyyyzzzz{{{{{||||}}}}}~~~~    ^_Z[\] 0WXTUV Y1ʌb`acˍdhfgiejlmkntupqrsov{|xyzw}~+t %O @ @ @ @ @r s   · ÷ ķ  !"#% $ )*, +[]^\!&'#$%"RTUS             #   ! 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Lariptioni J N'^2”eIG`<}sis generator...B.,v\U\o@G` 0game-reference subform1|C@a3-]n@pgame-referenceeSUnFJ ⩛|C@a3-gameid!hdRI3 ^2”eIG`<}sgameidd J۩c1%+՘@ 0game-game subset subform1nGsM U\"[p@ygame-game subseteneratorѴa|F5AL|욳[J7j1Qentered byM#MF./ԅyk2Zo@`E!peopletF,Kz1M#MF./ԅyname_QJe8r~UzM#MF./ԅyidУAљz@ܗ|욳[J7j1Qextensible-playerL~Jޘ)9g|욳[J7j1Qincludedqf;H8SS0IXu@`E!tobeincluded ,M7c3grqf;H8SSidnC-qf;H8K[v1b N  : k & W  C t/ @ @parentid ^@xnGsM U\childidq9g0MCҜ'ςO>;{nameB0 9CB0 2CB0 8CB0 10CB0 11CB0@ʇn@Referencesreference!hdRI3 'ςO>;{gameid<SELECT [game-game subset].parentid, [game-game subset].childid, game.name FROM game INNER JOIN [game-egame_1_name\sNfYH d5U`<abc"game_1.name_Labelgame_1.name"game_1_name_Label/HMOw`FormFootercPyMŀPerator$is_generhtmnoprz{mes Ariald2e12g237hghMS Sans Serifi1ghj1ghk1l23:m4n2o2p5r35zij?2H&~Y Detail^y%@o=m5F`a<b c, title titleB@NxCd`<a<bDctitle_Label titleR߮KD[ m5F`ab c,kauthorsauthorsGnXA Y Hd`<abDcauthors_Labelauthorsi#9Ao0Ԏ}m5F`ab ck$assignment details$assignment details$assignment_details#N 2d`<abDc0assig`$A`$1@Tppp@XAYq@\rrrWW\K&ll5l#-'' ','l FL 6 lL,  #\$  lL, 0 p  0   0   0 0  L.@<:L%\% $ |<(,'f ]>l5</ L( l<0 `  L(C"o<IBc(`wMS Sans Serif{5`FormHeader{]RK@].` Detail7o}MQ 1m7UF`taxb ce fNameNameUsO# !4d5U`<axbcname_LabelName MEIl]m 27UF`ta b'c e fkDescriptionDescriptionauDZAY2d5U`<a bc"description_LabelDescription]CC8p3`tahbK[& @ @ @ @'cd.game-reference subformFooter,WDT=n#";""d5]`<axb# cN#_*󝔆@jCH+comment6References Assigned to Jenn6References Assigned to Jenn Arial8$4hHP DeskJet 890C/MOSHEHOME/SessiXC od,,LetterDINU"4$ orm18Form.game-reference subform1 gameid gameid.game_reference_subform1:0L'j2]`aJbfiCheck16is generator FalseYt,#Jq˒@d5`a,bcLabel17Is generator{k}QLSLO:!up3U`abcDd2game-game subset subform1l5</ L( l<0 `  L( )t`T$  $(t`,P@<'8%'H%'X%:hme_subset_subform1@AI 3H1p3U`tabcDd0game-game subset subform:Form.game-game subset subformchildid gameid0game_game_subset_subform!kL[_`FormFooterCuO7\6orm!kL[_o5UDc`def,n,>I͏ Extensible?"extensible-actionTable/QueryExtensible_ YeF`a<b c,namename3wf Kœ†8d`<a<bDcname_Labelname./OGbm5F`abc,kdescriptiondescription)qDL d`<abDc"description_LabeldescriptionwFR(K^U@m5F`abc,kgenerategenerate7˻AU%d`<abDcgenerate_LabelgenerateG Ij`a(iextensible"extensible-actionlo#JbWTd`<a(bDc extensible_Labelextensible, IO\?#f`<a<bP Line11ZhNW/]f`"PageFooterSection| X)G;n'm;F`<abc,i j Text9 =Now()Long DateO8jFGtgbm;F`abc,i jk Text10K[1b N  : k & W  C t/ @ @H="Page " & [Page] & " of " & [Pages]f`D'@w`ReportFooter egi`lO0y_Labp3U`ta4bcd0game-game subset subform:Form.game-game subset subformchildid gameid0game_game_subset_subform.]Eڷ VWp3U`a4bc2game-game subset subform1;{͗՘@ DgamenGsM U\"[p@ Dgame-game subsetvnM.;FF'MnGsM U\R#>RAP)&id9bBgxWݘ՘@ 0game-reference subform2|C@a3-]n@game-referenceoNڽF5߾d|C@a3-referenceidreferencereference"[Event Procedure] Ariald2e12g237hghMS Sans Serifi1ghj1ghk1l23:m4n2o2p5r35zijMS@r* Ariald2e12g237hghzd5`aabcLabel17Is generatorMS Sans Serifi1ghj1ghk1l23:mmidalgorithmid8algorithm_referebel13jCheck14d Label15FormFooterassigned toTable/QueryVSELECT people.name, people.id FROM people; assigned_to"SELECT people.uperset Queryq9g0MCҜ ޿Cc]7uRgame.nameq9g0MCҜ ޿Cc]7uRgame_1.nameSuperset QuerySupeK~n@%Pn@GeneratorsGen K[Nrset Query Arial8$Dhsnoopy24C odXXLetter DINU"SSinclude...B.,v\@ 0game-reference subform1|C@a3-]n@ game-referenceeSUnFJ ⩛|C@a3-gameid!hdRI3 |욳[J7j1Qgameid\DE4ѽ3#՘@ 0game-game subset subformnGsM U\"[p@(Įgame-game subsetvnM.;FF'MnGsM U\parentidJCou0 `  Detailt?@-ACD          B !"$#%'&(*+,-./012 3)46789:;< 5       !"# $ & ' ( ) * + %!,!.!/!0!1!2!3!4!5!6!7!8!9!Again, very similar to inspection game. Let L be a set containing n points, R the collection of all subsets of L containing at most p points, and B the collection of all subsets of L. RED chooses a member of R; BLUE chooses a member of B. If the intersection of the chosen sets is nonempty, the payoffs are 0. Otherwise, the payoff to BLUE (from RED) is the size of the set chosen by BLUE.LVAL#H1D}$ P~?`}$}$}$}$ < }$`}$}$}$}$}$@}$x}$}$}$0}$0}$0}$0}$0}$ }$`}$}$}$}$         'Generators.game.namegame5Generators.game.description/Generators.game.generate/Generators.game.included=Generators.game.coding completeX}$P}$}$0}$(}$Q.x@ h}$}$ P}$`}$ V }$(AM `}$(AM }$(AM "}$(AM'}$(AM8PMGenerators}$  }$h}$}$(}$S|-x@game8 }$   }$( }$h}$}$8L)x@coding queue}$ `}$}$ }$}$ }$}$ }$}$  }$`}$Generators.name`}$+Generators.description}$%Generators.generate}$%Generators.included}$7Generators.[coding complete] }$}$`}$VMx }$(AM,VM`}$(AM}$(AMe }$(AM }$(AM gameGenerators`}$  }$ }$ ( }$ }$ X }$P }$ }$x }$  }$ }$`}$game.name}$game.description}$game.generate}$game.included }$+game.[coding complete] }$(AMXTM `}$(AM;}$(AM.i}$(AM.[}$(AM cgame  }$@}$ 2 }$H}$ b }$P}$ }$X}$ h}$`}$`}$}$}$}$ }$coding complete }$}$}$ (}$8}$P}$h}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$(}$h}$h}$ }$h}$ $}$h}$ $}$h}$  }$h}$ }$z }$p}$}$(KM`}$P}$ }$}$ }$}$}$}$0}$}$ P}$ }$ }$}$0}$<h}$p}$x}$}$}$P}$}$}$}$0}$h}$game }$ }$ 8}$#P}$tobeincludedgamePrimaryKeypeoplegame gameidh}$}$v h}$X}$G0}$}$}q$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$}$ }$8}$}$}$gameh}$}$ }$}$ }$}$ }$}$h}$}$}$H}$}$X}$}$h}$}$}$}$}$ }$&%game.[is generator] }$}$}$}$x}$}$ }$}$}$}$}$tobeincludedgame (}$ }$Mx,}$}$<}$ 0}$d}$8}$@}$ }$ }$}$8}$}$ h}$}$ @ h}$}$ }$}$8}LVAL$p}$p}$}$p}$}$h}$wYPPNgg Y dY includeidgsguYYY.rCidPrimaryKey77@am__gameid 'gamgame-game subset subform@8I=  am #gam am #b+rN  ,([__gameid] = childid)E __gameid 'game- 0@Equilibrium in Hotelling's Model of Spatial CompetitionM.J. Osborne and C. Pitchik@CxllO  LVALжcP=) y f R ? ???????????????????????????????????????, ˢˢˢˢˢˢˢˢˢˢˏ ˏˏˏˏˏˏˏˏe-reference subform2j2& ĝn@Fn@Tables~sq_fgame-reference subform1j2& ɘmn@5mn@Tables~sq_fgame-reference subformh2& [o@[o@Tables~sq_fgame-game subset subform1n2& eZo@:JZo@Tables~sq_fMany different but similar definitions have been given. In fact, even in the Osborne and Rubinstein text alone two definitions are given. The one I am choosing to generate is from the first H+D example given in O+R (since the second definition is just a combination of this def and prisoners dilemmas). Generate a two person symmetric game with payoff matrix B, B C, A A, C D, D with A > B > C > D ------------------------------------------------------ More broad definition: According to Johansson, can generate the following matrix for a 2-player game: (R-S)/2, (R-S)/2 0, R R, 0 Many different but similar definitions have been given. In fact, even in the Osborne and Rubinstein text alone two definitions are given. The one I am choosing to generate is from the first H+D example given in O+R (since the second definition is just a combination of this def and prisoners dilemmas). Generate a two person symmetric game with payoff matrix B, B C, A A, C D, D with A > B > C > D ------------------------------------------------------ More broad definition: According to Johansson, can generate the following matrix for a 2-player game: (R-S)/2, (R-S)/2 0, R R, 0 (R-F)/2, (R-F)/2 Can also mix up table by swapping order of the actions for either player. If generated with R > F > S > 0 then have a Prisoner s Dilemma (or near Prisoner s Dilemma without second condition met). If R < F then have Chicken Game. Can allow S to be 0 sometimes.]+m ^In proc 18-th ICML, 2001Friend-or-Foe Q-learning in general-sum games.Michael Littman@"}qq`000  LVALMR2ODBCTimeoutMaxRecordsRecordLocksRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL <       UKH[^ URAP)&\o@_referenceV㛃H/ӯonRAP)&titlek&%^) LѳeŷRAP)&authors LVALMR2ODBCTimeoutMaxRecordsRecordLocksRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL <       UKH[^ URAP)&\o@_referenceV㛃H/ӯonRAP)&titlek&%^) LѳeŷRAP)&authorsLVALhD pnzI p b?x nzpnzpnznz  nznznznznznznznz  )game-reference.gameidgame-reference3game-reference.referenceid@nz8nznznz nzn@nz(nz nz($ nz($game-referencenznznz nznz]n@7~sq_fgame-reference subform2(nz nznz nznznznznz($ nz($game-reference nz`nz nzhnznznz nznz nz nz8nz@nzHnzPnzXnzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzpnznzxnznz nz nz nz nz nz nzz X nznzx nzp$(nz8 nzp nz nz8 nzp nz0@ nzH nz8 nzp nz nzgame-reference nz nz( nz@ nzP nzreferenceid-referencegame-referencePrimaryKey gameid#gamegame-reference nznzv nzpnznznznznqznznznznznznznznznznznznznznznznznznznznznznznznznznznznznz pnznznzhnz"nzgame-referencePrimaryKeynznznz nznznznznznznzPnz nzj+zN        c@iRational and convergent Learning in Stochastic GamesMichael Bowling and Manuela VelosopppL  LVALMR2ODBCTimeoutMaxRecordsRecordLocksRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL <       UKH[^ URAP)&\o@_referenceV㛃H/ӯonRAP)&titlek&%^) LѳeŷRAP)&authors LVAL0hD 4  ?4444P4h4  4244444424  IGAMUT Games.game-game subset.parentidgame-game subsetGGAMUT Games.game-game subset.childid44484 H4cž@,X4p4@4h44& `'24&GAMUT Games444H4game-game subset444 4p4"[p@Y~sq_dGAMUT Games~sq_dgame-game subset subformp4 4X4 `44MGAMUT Games.[game-game subset].parentid4KGAMUT Games.[game-game subset].childid`44h4` 4&0ǂ124&game-game subseth4 44 x444`4 4&124& game-game subset F4@4 4H44`4h444__gameidh4 4404 H484@4H4P4X4444444444444444444444444444444444444444444444444444444444444x44`4 4 4 4 4 4z 444p&h4 44 44 4 4044 4 4 4game-game subsetH4`4x4444PrimaryKeyparentid)gamegame-game subset2)gamegame-game subset1'gamegame-game subset childid 44v 844H444q444444444444444444444444444444 44x44'4game-game subset444484 4p444 4H4x444)gamegame-game subset2(44 h4[__gameid]44444 4,4444)gamegame-game subset2p44448444 4v1Χb N~~~ ~Y Y Y Y  Y SectionStyleIDStyleIDSectionBackColorSpecialEffectqDqDDqqDqDDqqDqDDqYYYPrimaryKeySectionStyleIDsgRRRR%Y+idsAppwizSampleAppDocName345@F@j^RRRR/X*idsAppwizSampleAppDocName344 @^^RRRR'W'idsAppwizSampleAppDocName343|F03589|F03589 |T00478B@n`RRV'idsAppwizSampleAppDocName342|F03586|C02805 |T00483n`RRU)idsAppwizSampleAppDocName341p@^^RRRR'T(idsAppwizSampleAppDocName340 @^^RRRR'S'4idsAppwizSampleAppDocName339 |T00479@sgRRRR7 R&4idsAppwizSampleAppDocName338 |T00482P@sgRRRR% P$ idsAppwizSampleAppDocName336r@@j^RRRR/O# idsAppwizSampleAppDocName335@@j^RRRR'N" idsAppwizSampleAppDocName334@^^RRRR'M! 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PrimaryKey p `  @ @ x x PxPxPx"!"#"#0##h##"#0##h#$  LVALΟ܍ ̄ N NNN L LLLLLLLLLLLLLLLL p ppppppppppppppɻ@^ƔƔƔƔƔƔ55555555555555nnnnnnnnnnnnnjEjjjjŇ&&·zjx@Wx@coding queue9{@4|@ RFF:::::::8 @rΔu@Δu@~sq_cGenerators~sq_cText189@4MR2KeepLocal TbVVVVVVT `q0pΔu@0pΔu@~sq_cGenerators~sq_cCombo319@4MR2KeepLocal TdXXXXXXV `p Δu@0pΔu@~sq_cGenerators~sq_cgame-reference subform19 @4MR2KeepLocal Txxxxxxv `o Δu@ Δu@~sq_cGenerators~sq_cgame-game subset subform9 @4MR2KeepLocal Tzzzzzzx `SeZ_pu@_pu@~sq_cSets of Games~sq_cCombo269@4MR2KeepLocal Tj^^^^^^\ `SxHXu@xHXu@tobeincludedgame9BBBBBBBBBB@ 2Wu@0IXu@tobeincluded9@FFF:::::::8 @JG=wp@G=wp@Superset Query9@E}JJJ>>>>>>>< @IN0wp@_L=wp@Superset Query9?v@J}@bVVJ>>>>>>< `HTvp@Tvp@Subset Query9@.}FFF:::::::8 @Gvp@T wp@Subset Query9W;v@:@^RRF::::::8 `F`vp@Zvp@~sq_rgame-game subset96@4MR2KeepLocal TXLLLLLLJ `EZo@EZo@Sets of Games9@HHH<<<<<<<: @g|Yo@{曑u@Generators9#=x:H@"|@ ZNNB6666664 `#n@#n@Unassigned References9b@ XXXLLLLLLLJ @QÏn@gn@Unassigned References9-@@|@NpddXLLLLLLJ `Fn@tu@reference Query9@|@XLL@@@@@@@> @saϗn@saϗn@~sq_rAll References In List9x @P4MR2KeepLocal TdXXXXXXV `C^ϗn@C^ϗn@All References In List9v@VOZZZNNNNNNNL @:,?n@-?n@~sq_cgame-reference subform~sq_creferenceid9 @74MR2ODBCTimeoutMaxRecordsRecordLocksRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL <       My]NaνK0 ( U|욳[J7j1Q{曑u@h ]Generatorsq9g0MCҜ|욳[J7j1Qname{|N@٠Ym|욳[J7j1QdescriptionUE]=,J&ZbN|욳[J7j1QgenerateL~Jޘ)9g|욳[J7j1Qincluded LVALMR2 GUIDNameMapL H2AhvE(   UOs|NNI-cn@References Assigned to KevinV㛃H/ӯonOs|NNItitlek&%^) LѳeŷOs|NNIauthors㩻'O-sOs|NNIassignment details2LVAL д| |ʾ  łVhttp://citeseer.nj.nec.com/cache/papers/cs/26914/http:zSzzSzwww.people.Virginia.EDUzSz~cah2kzSzexpbooknsf.pdf/recipes-for-interactive-learning.pdfhttp://Part of collection "Game Theory as a Theory of Conflict Resolution" Not very useful to us because mainly about the social experimental type resultshttp://citeseer.nj.nec.com/cache/papers/cs/26914/http:zSzzSzwww.people.Virginia.EDUzSz~cah2kzSzexpbooknsf.pdf/recipes-for-interactive-learning.pdf This version of the book has a lot of chapters about games that are blank and marked as unfinished but would most likely be good to look at if a finished version appears soon.Investigate complexity of finding pure strategy nash equilibria. Essentially, they do this for graphical games - this is a slight of hand, since they're restricting the input size in order to get results. They also present some tractable cases.Describe hotellings game - infinite, extensive form, quite nice. Show how to solve a _subgame_ of it by solving a system of "highly non-linear" equations - can only be done approximately. Wouldn't count that as an algorithm.Motivated by free-flight common payoff. The result really holds only for games of incomplete information (they have possible worlds there :) ) Have a reduction from SAT, but the games are not the ones we're interested in.A listing of the 57 conflict games is given by Brahms in "Omniscience and Omnipotence: How they may Help - of Hurt - in a Game" (Inquiry 25-2 1982. p217-31). and also in Superior Beings: if tThe Exist, How would we Know? Game theoretic Implications of Omnisience, Omnipotence, Immortality, and Incomprehensibility. (New York, Springer-Verlag, 1983) and Theory of Moves (Cambridge University Press, Cambridge, 1994) from http://www.economics.laurentian.ca/strategic_think.27/modules/course_schedule.98/2x2%20games/typology_of_%202x2.htmJournal of Peace Science 2, p 171-203. found on http://www.economics.laurentian.ca/strategic_think.27/modules/course_schedule.98/2x2%20games/typology_of_%202x2.htm LVAL %%%%     SS"S#S$S%S&S'~~~ ~!~"~#~$~%~&~ '~ (~ )~ *~ +~,~-~.~/~0~1~2~3~4~5~6~7~8~9~:~;~<~=~ >~!?~"@~#A~$B~%C~&D~'E~(F~)G~*H~+I?J?K?L?M?N?O?P?Q?R? S? T? U? V? W?X?Y?Z?[?\?1 !"#'$K%QSgSkSqSuSSSSSS S S S FSJS fSlSSSSSSSSSSSSS#S!<SRS]S MR2.ValidationRuleValidationTextOrientation FilterOrderByOrderByOnNameMapDefaultViewGUIDColumnWidthColumnOrderColumnHiddenDescription FormatInputMaskCaptionDefaultValueRequiredAllowZeroLengthDisplayControlIMEModeIMESentenceMode$UnicodeCompressionDecimalPlaces    U+_I9$ @PfCDU@N6ˠ,Uo@algorithmܹT@Av  _Values of Smooth Non-Atomic Games: The Method of Multilinear Approximation in The Shapley ValueguThe Strategy of Conflict _Team Games As Models of Intergroup Conflicts4&uSufficiency Conditions for Nash Equilibrium in N-Person Differential GamesR_Simulated annealing of games equilibria.1 uPure Nash Equilibria: Hard and Easy Games1_On the np-completeness of finding an optimal strategy in games with common payoffsZBOmniscience and Omnipotence: How they may Help - of Hurt - in a GameL_Nash propagation for Loopy Graphical Games2_Multi-Agent Reinforcement Learning: Theoretical Framework and an AlgorithmR"uIterative Solution of Games by Ficticious Play6 _Graphical Models for Game Theory( BGeometric Games and Their Applications. BGames of StrategyBFriend-or-Foe Q-learning in general-sum games.6_Equilibrium in Hotelling's model of competition7 _Efficient Nash Computation in Large Population Games with Bounded InfluenceSBDeception in 2 X 2 Games  _Bounding the ineffic AValues of Smooth Non-Atomic Games: The Method of Multilinear Approximation in The Shapley ValueMonderer, Neyman@"}}k  +N   ||||~~~~   ʌb`acˍdhfgiejlmk}~EGHFRVTUWSX\Z[]Y^sk/~-zn@-zn@~sq_falgorithm9< @4MR2KeepLocal TJ>>>>>>< `j -zn@/~-zn@~sq_calgorithm~sq_calgorithm-reference Subform19 @4MR2KeepLocal @@`  @  `@ @ @ @ E@ @ EB    `9B    `9 Local-Effect Games:@Leyton-Brown, TennenholtzEE* +pO%W R  ) 2 n -> Times New Roman CEl??POL Haettenschweiler -> Arial Narrow CEh??POL Arial -> Arial CED??KOR: Tahoma -> GulimB??KOR Times New Roman -> GulimR??KOR MS Sans Serif -> GulimN??KOR Haettenschweiler -> GulimT??KOR Arial -> Gulim>??JPN: Tahoma -> Ms PgothicL??JPN Times New Roman -> MS Pminchol^??JPN MS Sans Serif -> Ms PgothicX??JPN Haettenschweiler -> Ms Pgothic^??JPN Arial -> Ms PgothicH?  ?HBR Times New Roman -> Arial (Hebrew)d? ?HBR MS Sans Serif -> TahomaP?  ?HER Haettenschweiler -> Arial (Hebrew)h?  ?HBR Arial -> Arial (Hebrew)P? ?GRK Times New Roman -> Times New Roman Greekr? ?GRK Ms Sans Serif -> Arial GreekZ? ?GRK Haettenschweiler -> Times New Roman Greekt? ?GRK Arial -> Arial GreekJ? ?CZE Times New Roman -> Times New Roman CEl? ?CZE Haettenschweiler -tTheory of Games and Economic Behavior-uThe Strategy of Conflict _The Complexity of two-person zero-sum games in extensive form.F&uSufficiency Conditions for Nash Equilibrium in N-Person Differential GamesR$uSome Topics in Two-Person Games'_Simulated annealing of games equilibria.1 uPure Nash Equilibria: Hard and Easy Games1_On the np-completeness of finding an optimal strategy in games with common payoffsZ_Nash propagation for Loopy Graphical Games2uNash Equilibrium with Strategic Complementarities9uNash Equilibrium in Oligopoly Games with Monotone Best ResponsesHuMinimizing a Submodular Function on a Lattice5"uIterative Solution of Games by Ficticious Play6 _Graphical Models for Game Theory(uGames and Decisions uExotic Phenomena in Games and Duopoly Models4uEquilibrium Points in Nonzero-Sum N-Person Supermodular GamesE_Efficient Computation of Equilibria for Extensive Two-Person GamesJDynamic Noncooperative Game Theory*uDynamic Games of Innovation#%uDifferential Games_A polynomial time nash equilibriu Equilibrium Points in Nonzero-Sum N-Person Supermodular GamesTopkisQQQI <+LN^^```` A General Theory of Equilibrium Selection in GamesHarsanyi, Seltonbook Jackson HB145 .H38 1988ooP> ^+nEI) / B p uThe Strategy of Conflict _Team Games As Models of Intergroup Conflicts4_Simulated annealing of games equilibria.1 uPure Nash Equilibria: Hard and Easy Games1_On the np-completeness of finding an optimal strategy in games with common payoffsZBOmniscience and Omnipotence: How they may Help - of Hurt - in a GameL_Nash propagation for Loopy Graphical Games2_Multi-Agent Reinforcement Learning: Theoretical Framework and an AlgorithmR"uIterative Solution of Games by Ficticious Play6 _Graphical Models for Game Theory( BGeometric Games and Their Applications. BGames of StrategyBFriend-or-Foe Q-learning in general-sum games.6_Equilibrium in Hotelling's model of competition7 _Efficient Nash Computation in Large Population Games with Bounded InfluenceSBDeception in 2 X 2 Games  _Bounding the inefficiency of equi NA Taxonomy of 2X2 GamesRapoport and Guyer In General Systems vol.11 (1966): 205 Jackson H9.G4nn7# U+eEI) / B p ````uThe Strategy of Conflict _Team Games As Models of Intergroup Conflicts4_Simulated annealing of games equilibria.1 uPure Nash Equilibria: Hard and Easy Games1_On the np-completeness of finding an optimal strategy in games with common payoffsZBOmniscience and Omnipotence: How they may Help - of Hurt - in a GameL_Nash propagation for Loopy Graphical Games2_Multi-Agent Reinforcement Learning: Theoretical Framework and an AlgorithmR"uIterative Solution of Games by Ficticious Play6 _Graphical Models for Game Theory( BGeometric Games and Their Applications. BGames of StrategyBFriend-or-Foe Q-learning in general-sum games.6_Equilibrium in Hotelling's model of competition7 _Efficient Nash Computation in Large Population Games with Bounded InfluenceSBDeception in 2 X 2 Games  _Bounding the inefficienc SDeception in 2 X 2 GamesSteven J. BrahmsJournal of Peace Science 2, p 171-203. 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m  [PLID      0   m[SLID      0   mMR26OrderByOn"DatasheetFontName&DatasheetFontHeight&DatasheetFontWeight&DatasheetFontItalic,DatasheetFontUnderlineTabularCharSetTabularFamilyOrientation$DatasheetForeColorNameMapColumnWidthColumnOrderColumnHiddenRequiredAllowZeroLengthDisplayControl$UnicodeCompressionGUID   Arial      "     U ZjjM9 FontID      bFontName         m bComments  &     tTheory of Games and Economic Behavior-uThe Strategy of Conflict _The Complexity of two-person zero-sum games in extensive form.F&uSufficiency Conditions for Nash Equilibrium in N-Person Differential GamesR$uSome Topics in Two-Person Games'_Simulated annealing of games equilibria.1 uPure Nash Equilibria: Hard and Easy Games1_On the np-completeness of finding an optimal strategy in games with common payoffsZ_Nash propagation for Loopy Graphical Games2uNash Equilibrium with Strategic Complementarities9uNash Equilibrium in Oligopoly Games with Monotone Best ResponsesHuMinimizing a Submodular Function on a Lattice5"uIterative Solution of Games by Ficticious Play6 _Graphical Models for Game Theory(uGames and Decisions uExotic Phenomena in Games and Duopoly Models4uEquilibrium Points in Nonzero-Sum N-Person Supermodular GamesE_Efficient Computation of Equilibria for Extensive Two-Person GamesJDynamic Noncooperative Game Theory*uDynamic Games of Innovation#%uDifferential Games_A "Exotic Phenomena in Games and Duopoly ModelsDavid RandJournal of Mathematical Economics 5 (1987)ppD8 +pO%W R  ) 2  @ @ @ @ @ @ @ @ @ @ @ )*, +[]^\!&'#$%"RTUS  7 = > 9 : ; < 8 ? D E F G H @ T | } ~         U U U Uiuvwxyz~./0UVWXYZڈډڊڋtTheory of Games and Economic Behavior-uThe Strategy of Conflict _The Complexity of two-person zero-sum games in extensive form.F&uSufficiency Conditions for Nash Equilibrium in N-Person Differential GamesR$uSome Topics in Two-Person Games'_Simulated annealing of games equilibria.1 uPure Nash Equilibria: Hard and Easy Games1_On the np-completeness of finding an optimal strategy in games with common payoffsZ_Nash propagation for Loopy Graphical Games2uNash Equilibrium with Strategic Complementarities9uNash Equilibrium in Oligopoly Games with Monotone Best ResponsesHuMinimizing a Submodular Function on a Lattice5"uIterative Solution of Games by Ficticious Play6 _Graphical Models for Game Theory(uGames and Decisions uExotic Phenomena in Games and Duopoly Models4uEquilibrium Points in Nonzero-Sum N-Person Supermodular GamesE_Efficient Computation of Equilibria for Extensive Two-Person GamesJDynamic Noncooperative Game Theory*uDynamic Games of Innovation#%uDifferential Games_A polynomial time nash equilibrium algorithm for rep Games and DecisionsLuce, Raiffabook>3- {+pO%W R  ) 2       -./0123456 7 8 9 : +           !"#$%&'()*+ , - . / 0123456789:<           ; !"#$% & ' ( ) *+,.tTheory of Games and Economic Behavior-uThe Strategy of Conflict _The Complexity of two-person zero-sum games in extensive form.F&uSufficiency Conditions for Nash Equilibrium in N-Person Differential GamesR$uSome Topics in Two-Person Games'_Simulated annealing of games equilibria.1 uPure Nash Equilibria: Hard and Easy Games1_On the np-completeness of finding an optimal strategy in games with common payoffsZ_Nash propagation for Loopy Graphical Games2uNash Equilibrium with Strategic Complementarities9uNash Equilibrium in Oligopoly Games with Monotone Best ResponsesHuMinimizing a Submodular Function on a Lattice5"uIterative Solution of Games by Ficticious Play6 _Graphical Models for Game Theory(uGames and Decisions uExotic Phenomena in Games and Duopoly Models4uEquilibrium Points in Nonzero-Sum N-Person Supermodular GamesE_Efficient Computation of Equilibria for Extensive Two-Person GamesJDynamic Noncooperative Game Theory*uDynamic Games of Innovation#%uDifferential Games_A polynomial time n 36@Graphical Models for Game TheoryM. Kearns and M. Littman and S. Singh___8 ^+npO%W R  ) 2      #$% & ' ( ) *+,./0123456789 : ; < = >?@-ACD          B !"$#%'&(*+,-./012 3)46789:;< 5      tTheory of Games and Economic Behavior-uThe Strategy of Conflict _The Complexity of two-person zero-sum games in extensive form.F&uSufficiency Conditions for Nash Equilibrium in N-Person Differential GamesR$uSome Topics in Two-Person Games'_Simulated annealing of games equilibria.1 uPure Nash Equilibria: Hard and Easy Games1_On the np-completeness of finding an optimal strategy in games with common payoffsZ_Nash propagation for Loopy Graphical Games2uNash Equilibrium with Strategic Complementarities9uNash Equilibrium in Oligopoly Games with Monotone Best ResponsesHuMinimizing a Submodular Function on a Lattice5"uIterative Solution of Games by Ficticious Play6 _Graphical Models for Game Theory(uGames and Decisions uExotic Phenomena in Games and Duopoly Models4uEquilibrium Points in Nonzero-Sum N-Person Supermodular GamesE_Efficient Computation of Equilibria for Extensive Two-Person GamesJDynamic Noncooperative Game Theory*uDynamic Games of Innovation#%uDifferential Games $Iterative Solution of Games by Ficticious PlayG. W. Brownin "Activity Analysis of Production and allocation"||G: a+qEI) / B p uThe Strategy of Conflict _Team Games As Models of Intergroup Conflicts4_Simulated annealing of games equilibria.1 uPure Nash Equilibria: Hard and Easy Games1_On the np-completeness of finding an optimal strategy in games with common payoffsZBOmniscience and Omnipotence: How they may Help - of Hurt - in a GameL_Nash propagation for Loopy Graphical Games2_Multi-Agent Reinforcement Learning: Theoretical Framework and an AlgorithmR"uIterative Solution of Games by Ficticious Play6 _Graphical Models for Game Theory( BGeometric Games and Their Applications. BGames of StrategyBFriend-or-Foe Q-learning in general-sum games.6_Equilibrium in Hotelling's model of competition7 _Efficient Nash Computation in Large Population Games with Bounded InfluenceSBDeception in 2 X 2 Games  _Bounding the inefficiency of equilib [Games of StrategyMelvin DresherJackson QA270 .D7 (and mathcs)MM- X+hEI) / B p uThe Strategy of Conflict _Team Games As Models of Intergroup Conflicts4_Simulated annealing of games equilibria.1 uPure Nash Equilibria: Hard and Easy Games1_On the np-completeness of finding an optimal strategy in games with common payoffsZBOmniscience and Omnipotence: How they may Help - of Hurt - in a GameL_Nash propagation for Loopy Graphical Games2_Multi-Agent Reinforcement Learning: Theoretical Framework and an AlgorithmR"uIterative Solution of Games by Ficticious Play6 _Graphical Models for Game Theory( BGeometric Games and Their Applications. BGames of StrategyBFriend-or-Foe Q-learning in general-sum games.6_Equilibrium in Hotelling's model of competition7 _Efficient Nash Computation in Large Population Games with Bounded InfluenceSBDeception in 2 X 2 Games  _Bounding the inefficiency o YGeometric Games and Their ApplicationsW. H. Rucklestarted this, need to dig out more examples of gamesvv@2  "N;;Compact representationx@Z* "999999 ____id ' ,Lookup_propertyid.nameE property-referenceLookup_propertyidl@`Matrix Game@Z "@~Rddcategory-reference111 reference referencecategory-referenceZ@=OC ?@[category-reference].referenceidY 3"reference.authors; 3reference.title7 3 Symmetricb@Z "<<<<<<<<  !  !referenceidcategory-re  !categoryidgame-categorycategoryidgame-category Subform1.categoryid\H..  !gameidZero-SumSymmetricMatrix GameZero-SumF@Z+EI) / B p uThe Strategy of Conflict _Team Games As Models of Intergroup Conflicts4_Simulated annealing of games equilibria.1 uPure Nash Equilibria: Hard and Easy Games1_On the np-completeness of finding an optimal strategy in games with common payoffsZBOmniscience and Omnipotence: How they may Help - of Hurt - in a GameL_Nash propagation for Loopy Graphical Games2_Multi-Agent Reinforcement Learning: Theoretical Framework and an AlgorithmR"uIterative Solution of Games by Ficticious Play6 _Graphical Models for Game Theory( BGeometric Games and Their Applications. BGames of StrategyBFriend-or-Foe Q-learning in general-sum games.6_Equilibrium in Hotelling's model of competition7 _Efficient Nash Computation in Large Population Games TOmniscience and Omnipotence: How they may Help - of Hurt - in a GameSteven J. BrahmsThere seems to be about 80 journals called Inquiry or with Inquiry in the title... No idea which of these we actually want8@CbP  LVAL"Each of n people chooses whether or not to become a political candidate, and if so which position to take. There is a continuum of citizens, each of whom has a favorite position; the distribution of favorite positions is given by a density function f on [0, 1] with f(x) > 0 for all x in [0,1]. A candidate attracts the votes of those citizens whose favorite positions are closer to his position than to the position of any other candidate; if k candidates choose the same position then each receives the fraction 1/k of the votes that the position attracts. The winner of the competition is the candidate who receives the most votes. Each person prefers to be the unique winning candidate than to tie for first place, prefers to tie for first place than to stay out of the competition, and prefers to stay out of the competition than to enter and lose." LVAL "Two animals are fighting over some prey. Each can behave like a dove or like a hawk. The best outcome for each animal is that in which it acts like a hawk while the other acts like a dove; the worst outcome is that in which both animals act like hawks. Each animal prefers to be hawkish if its opponent is dovish and dovish if its opponent is hawkish." Using certain definitions of the values of payoffs under certain restrictions, this game can become Prisoner's Dilemma or Chicken. Has an evolutionarily stable strategy.+N22D qotI ` ?qoqo qo8qoO $qoqoqo$qoLqo|qoqoqo qo$qoqoqoqo8qohqoqoqoqo$qoqoqoqoqoqoqoqoqo$qoqoqo$qoLqo|qoqoqo qo                 reference.titlereferencereference.bibtexreference.id!reference.authors)reference.assigned to7reference.assignment detai n@wzn@~sq_freference9 @4MR2KeepLocal TJ>>>>>>< ` n@ n@~sq_creference~sq_cCombo309@w4MR2KeepLocal TbVVVVVVT ` n@ n@~sq_creference~sq_ccategory-reference subform9 @v4MR2KeepLocal T||||||z `ֹn@ֹn@~sq_creference~sq_cproperty-reference subform9C @u4MR2KeepLocal T||||||z ` @@` @   `@@@"@@"@H @ 9@H @ 9 Game TheoryGuillermo OwenGame Theory (I)Guillermo Owen@ THH8''  LVAL{tmf_XQJC<5.'  xqjc\UNG@92+$ | u n g ` Y R )pZero-Sum Games )Welfare Game0Weak Dispersion GamespWar of attrition6pUniform Local-Effect Game with clique-Uniform Local-Effect Game!!)Unbalanced Game#)Tree Structured Game)Traveler's Dilemma 0Symmetric Binary Global Games%pStag and Hare-)Soccer Game)Small Pig)Simplified Poker)Simple Point Catcher Game!)Simple Inspection Game 3Simple Ambush Game%)Shapley's Game0Selfish Dispersion Games pSecond price auctions formulated as strategic game:pSAT Games)Rock, Paper, ScissorspRoad GamepRing structured game()Random GamesPrisoner's DilemmapPotential Games0Partial Dispersion Games +)Parallel Network GamespN-Player Prisoner s Dilemma&)N-Player Chicken*)Network GamesAccording to Cooper at al. they are symmetric games "which exhibit multiple Nash eqilibria which are Pareto-rankable" However, there is a footnote to Thomas Schelling, The Strategy of Conflict, which states that he used the term to refer to games in which the multiple Nash eq yielded identical payoffs. Also called "collaboration games." We will use the Pareto-optimal def and also make "collaboration games" available --------------------------------------- Agents have common payoffs or should coordinate to get their highest payoffs. In 2x2 games, have three equilibria: - two symmetric equilibria in pure strategies - one symmetric equilibrium in mixed strategies\LVALlN ͫ0 k k ' '''''''''''''''''''''''''''''''˶ Q QQQQQQQQQQډȚ?UJ`QUJ`QUJ`QkoLkQm'UJ`QUJ`QUJ`QkoLkQm8'UJ`QUJ`QUJ`QkoLkQm:'UJ`QUJ`QiQSQiQbMQ'ά~^` u*algorithmalgorithm-{referencereference8algorithm-referencealgorithm-referencegame-referencegame-reference l!peoplepeopleU\game-game subsetgame-game subsetDtobeincludedtobeincluded94prioritypriority?fgamegame,Jgame_1game&game_2gameЃσσσσσσσσσσσσσσσσσσσσσ0 ͫ0 k k ' '''''''''''''''''''''''''''''''˶ Q QQQQQQQQQQډ&&&&&&&&&&&&&&&&&&&&ȻZƄƄƄƄƄA@}@}T@T@~sq_cGAMUT GT@T@dcž@dcž@~sq_dGAMUT Games~sq_dCombo269@4MR2KeepLocal TfZZZZZZX `dcž@dcž@~sq_dGAMUT Games~sq_dCombo269@4MR2KeepLocal TfZZZZZZX `dcž@dcž@~sq_dGAMUT Games~sq_dCombo269@4MR2KeepLocal TfZZZZZZX `#T@#T@~dcž@dcž@~sq_dGAMUT Games~sq_dCombo269@4MR2KeepLocal TfZZZZZZX `#T@#T@~sdcž@dcž@~sq_dGAMUT Games~sq_dCombo269@4MR2KeepLocal dcž@dcž@~sq_dGAMUT Gdcž@dcž@~sq_dGAMUT Games~sq_dCombo269@4MR2KeepLocal TfZZZZZZX `~G S@G S@GAMUT Generators9R@DNNNBBBBBBB@ @}P@P@GAMUT References9.@NNNBBBBBBB@ @|4۟O@4۟O@GAMUT Games9@n DDD88888886 @zgN@gN@GAMUT Algorithms94@'NNNBBBBBBB@ @y0~x@~x@~sq_cgenerator coding queue~sq_cCombo109P@4MR2KeepLocal T|ppppppn `tYu@F\u@~sq_cAssigned References~sq_cassigned to9Y@4MR2KeepLocal T~rrrrrrp `jkSuu@kSuu@generator coding queue9|@:.ZZZNNNNNNNL @/hE#[o@hE#[o@Sets of Games9 @.HHH<<<<<<<: @.V)[o@V)[o@List All Generators9@.TTTHHHHHHHF @[o@[o@~sq_fgame-game subset subform19 @C4MR2KeepLocal Tj^^^^^^\ `[o@[o@game-game subset subform19@.```TTTTTTTR @eZo@:JZo@~sq_fgame-game subset subform9 @F4MR2KeepLocal Th\\\\\\Z `TZo@TZo@game-game subset subform9@0 ^^^RRRRRRRP @zLZo@"[p@game-game subset9@ NNNBBBBBBB@ @uZo@.Zo@~sq_calgorithm~sq_cCombo79@4MR2KeepLocal T`TTTTTTR `M1Zo@M1Zo@peoplealgorithm9@@@@@@@@@@> ʂZo@ʂZo@peoplegame966666666664 0Yo@Bkx@Sets of Games9@5@4|@ `TTH<<<<<<: `4O @ @ @ @ @ @ @ @ @ @ @ @ @ 33334$4$4$4$4$4$5$5$ 5$5$ 5$ 5$7$7$7$7$7$F FFF F F FF GG4AG4BG4CG4=G4>G4?G4@G 4DG 4EGIFIIIIIIII I IGKnKrKpKqKsKoLtLxLvLwLyLuMzM~M|M}M{NNNNYYYYYYYYZZZZZnrnvntnunwnsoxo|ozo{o}oyp~pԂpԀpԁpԃpqԄqԈqԆqԇqԅrԉrԍrԋrԌrԊtԣtԧtԥtԦtԤyyyyy{s{w{u{v{x{t|y|}|{|||~|z}}}}}}v177777  + HGame Theory As a Theory of Conflict ResolutionA. Rapaport (Ed.):@3YMM:  ~+N>> PPrisoner's Dilemma - Recollections and ObservationsAnatol Rapoport,@ C\PP?  +{tmf_XQJC<5.'  xqjc\UNG@92+$B ___________________ _ _ _ _ _________&u%u$u#u"u!u uuuuuuuuuu QBraithwaite's Arbitration SchemeD. Marc Kilgour@I==,  +{tmf_XQJC<5.'  xqjc\UNG@92+$BB ___________________ _ _ _ _ _________&u%u$u#u"u!u uuuuuuuuuuu IModels of Strategic RationalityReinhard Selten@"H<<+  h+x `V@Quantal Response Equilibria for Normal Form GamesR.D. McKelvey, T.R. Palfrey@rffI  0+@ XAn Introduction to Linear Programming and Matrix Game TheoryM. J. FryerHas some game matrices but none of them are particularly interesting for any reasonUH +QN  WAlgorithms for GamesAdelson-Velsky, Arlazarov, DonskoyR@"PDD  ?+OpO%W R  ) 2 %%%%%%% %%\\\\\\\\\\5\'\P\"\ P\"\ P\$\ P\$\ P\$\ P\$\ P\$\ P\$\ P\$\ P\$\  P\$\  P\$\  P\$\  P\$\  P\$\ P\$\ P\$\ P\$\ P\$\ P\$\ \z (\*\05\(\@*\ *\x;X \p\\\#\\z H)\h5\p)\ *\<P \\#\\ %\P\0%\\@%\\P%\\`%\0 \p%\h \%\ \%\ \%\!\%\H!\%\!\%\!\%\!\%\("\&\`"\&\"\ &\p\\\\P\\\\0 \h \ \ \!\H!\!\!\!\("\`"\"\xS(\(\(\(\ (\((\0(\8(\@(\H(\P(\X(\`(\h(\p(\x(\(\(\(\(\*\p\\\\P\\\\0 \h \ \ \!\H!\!\!\!\("\`"\"\'"\$\tblSectionStyles)\ )\0)\ StyleID SectionPrimaryKeytblControlStyles)\)\ )\*\SectionStyleIDPrimaryKey FontIDControlType "\0*\(\ $\P*\*\"\``*\PrimaryKey*\\vtTheory of Games and Economic Behavior-uThe Strategy of Conflict _The Complexity of two-person zero-sum games in extensive form.F&uSufficiency Conditions for Nash Equilibrium in N-Person Differential GamesR$uSome Topics in Two-Person Games'_Simulated annealing of games equilibria.1 uPure Nash Equilibria: Hard and Easy Games1_On the np-completeness of finding an optimal strategy in games with common payoffsZ_Nash propagation for Loopy Graphical Games2uNash Equilibrium with Strategic Complementarities9uNash Equilibrium in Oligopoly Games with Monotone Best ResponsesHuMinimizing a Submodular Function on a Lattice5"uIterative Solution of Games by Ficticious Play6 _Graphical Models for Game Theory(uGames and Decisions uExotic Phenomena in Games and Duopoly Models4uEquilibrium Points in Nonzero-Sum N-Person Supermodular GamesE_Efficient Computation of Equilibria for Extensive Two-Person GamesJDynamic Noncooperative Game Theory*uDynamic Games of Innovation# ;L@On the np-completeness of finding an optimal strategy in games with common payoffsChu and J. Halpern@C~~j  +N  !referenceidalgorithm- tOgame.name+  tOd&game.[is generator]A tOgame Ogame.gameid/ 3O \Game Theory and Experimental GamesAndrew Coleman>>>. w+jY,  V  D _ "  w I  _  z]xQ{GTheory of Games and Economic Behavior-uThe Strategy of Conflict uThe Set of Nash Equilibria of a Supermodular Game Is a Complete LatticeO&uSufficiency Conditions for Nash Equilibrium in N-Person Differential GamesR_Stability in Competition $uSome Topics in Two-Person Games'uSelection Criteria in Coordination Games: Some Experimental ResultsKuRationalizability, Learning, and Equilibrium in Games with Strategic Complementarities^_R.W. Rosenthal uPure Nash Equilibria: Hard and Easy Games1_Potential GamesuNash Equilibrium with Strategic Complementarities9uNash Equilibrium in Oligopoly Games with Monotone Best ResponsesH_Multi-Agent Reinforcement Learning: Theoretical Framework and an AlgorithmR_Multi-Agent Influence Diagrams for Representing and Solving GamesI_Multi-Agent Algorithms for solving graphical games:uMonotone Comparative Strategies'uMixed Equilibria in Games of Strategic Complements are UnstableGuMinimizing a Submodular Function on a Lattice5uLocal-Effect Games"uIterative Solution of Games by Ficticious Play6 _Graphical Models for Game Theory(uGames and DecisionsuGame Theory and Agents uGame Theory uGame Theory uExotic Phenomena in Games and Duopoly Models4!uExistence of Nash Equilibrium in N-Person Games without QuasiconcavityN uEquilibrium points in N-person games,uEquilibrium Points in Nonzero-Sum N-Person Supermodular GamesE_Equilibrium in Hotelling's model of competition7 _Efficient Nash Computation in Large Population Games with Bounded InfluenceSDynamic Noncooperative Game Theory*uDynamic Games of Innovation#%uDifferential GamesuComputing Supergame Equilibria&_Complexity Results about Nash Equilibria0 _Bounding the inefficiency of equilibria in nonatomic congestion gamesM#uAn Iterative Method of Solving a Game-uAn Experimental Study of N-Person Iterated Prisoner's Dilemma GamesKuA General Theory of E .@A Class of Games Possessing Pure-Strategy Nash EquilibriaR.W. RosenthalaaaQ a+q _B@ A Simple Adaptive Procedure Leading to Correlated EquilibriumS. Hart, A. Mas-Colell@"ymmU  22Wu@Wu@tobeincluded9::::::::::8 Rvr@vr@~sq_cGenerators~sq_cText189@4MR2KeepLocal TbVVVVVVT `QOvr@vr@~sq_cGenerators~sq_cgame-reference subform19y @4MR2KeepLocal Txxxxxxv `PTur@Ovr@~sq_cGenerators~sq_cgame-game subset subform9 @4MR2KeepLocal Tzzzzzzx `O tr@ur@~sq_cGenerators~sq_cgame-game subset subform19x @4MR2KeepLocal T||||||z `JG=wp@G=wp@Superset Query9@E}JJJ>>>>>>>< @IN0wp@_L=wp@Superset Query9?v@J}@bVVJ>>>>>>< `HTvp@Tvp@Subset Query9@.}FFF:::::::8 @Gvp@T wp@Subset Query9W;v@:@^RRF::::::8 `F`vp@Zvp@~sq_rgame-game subset96@4MR2KeepLocal TXLLLLLLJ `EZo@EZo@Sets of Games9@ HHH<<<<<<<: @g|Yo@l˹Xp@Generators9@`@"l|@ZNNB6666664 `#n@#n@Unassigned References9b@ XXXLLLLLLLJ @QÏn@gn@Unassigned References9-@A@K}|@NpddXLLLLLLJ `Fn@PFn@reference Query9{@@ |@ NdXXL@@@@@@> `saϗn@saϗn@~sq_rAll References In List9x @P4MR2KeepLocal TdXXXXXXV `C^ϗn@C^ϗn@All References In List9v@VOZZZNNNNNNNL @:,?n@-?n@~sq_cgame-reference subform~sq_creferenceid9 @74MR2KeepLocal Txxxxxxv `-n@n@~sq_fgame-reference subform29J @4MR2KeepLocal TfZZZZZZX `In@In@peoplereference9@@@@@@@@@@> %Jn@%Jn@References Assigned to Kevin9p@BfffZZZZZZZX @un@un@References Assigned to Alex9n@dddXXXXXXXV @+pO%W R  ) 2 wwwwwwwwwwwwwwwwwwww~ww~ww~ww~ww}ww}ww}ww}ww}wwqwwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwowwqww}ww}www w .Fww ww}wwwww G wwwwwwww} w wwwwwww G wwwwwwwwpw} wwwwwwwwww MR2ODBCTimeoutMaxRecordsSccStatusReplicableGUIDRecordLocksRecordsetType FilterOrderByOrderByOnOrientationNameMapDOL  < P84V        UܝP84V3*7@h_tblFieldTypesP84Vt@h_tblFieldsP84VP84VFieldIDP84VܝP84VFormatQ͗,`BܝP84VDecimalPlacesP84VܝP84VDefaultValueP84VܝP84VValidationRuleP84VܝP84VValidationTextP84VMR2 ANSI Query ModeAccessVersion6Track Name AutoCorrect InfoProjVerApptitle&StartupShowDBWindow(StartupShowStatusBarWizardVersion   09.50  Z RMicrosoft Access Wizards Application Data   jiMR2^OrientationOrderBytTheory of Games and Economic Behavior-uThe Strategy of Conflict _The Complexity of two-person zero-sum games in extensive form.F&uSufficiency Conditions for Nash Equilibrium in N-Person Differential GamesR$uSome Topics in Two-Person Games'_Simulated annealing of games equilibria.1 uPure Nash Equilibria: Hard and Easy Games1_On the np-completeness of finding an optimal strategy in games with common payoffsZ_Nash propagation for Loopy Graphical Games2uNash Equilibrium with Strategic Complementarities9uNash Equilibrium in Oligopoly Games with Monotone Best ResponsesHuMinimizing a Submodular Function on a Lattice5"uIterative Solution of Games by Ficticious Play6 _Graphical Models for Game Theory(uGames and Decisions uExotic Phenomena in Games and Duopoly Models4uEquilibrium Points in Nonzero-Sum N-Person Supermodular GamesE_Efficient Computation of Equilibria for Extensive Two-Person GamesJDynamic Noncooperative Game Theory*uDynamic Games of Innovation#%uDifferential Games_A polynomial time nash equilibriu *Theory of Games and Economic BehaviorVon Neumann, MorgensternbookQQK1 2QO1UJ`QUJ`QUJ`QkoLkQm'1UJ`QUJ`QUJ`QkoLkQm8'1UJ`QUJ`QUJ`QkoLkQm:'1 UJ`QUJ`QiQSQiQbMQ'1fQdf^QJ^UdiYmW`1fQdf^QUJ`Q1fQdf^QiQSQiQbMQ1iQSQiQbMQJ^UdiYmW`iQSQiQbMQO1iQSQiQbMQUJ`QiQSQiQbMQ;1F3+N]] %An Iterative Method of Solving a GameJulia Robinson@"MAA1  LVALGenerate a matrix of payoffs for one player (common payoff so all others are the same) where all of the highest payoffs occur on the diagonal. --------------------------------------------------------------------------- For two players, can generate a payoff matrix a, w b, x c, y d, z such that a > c d > b w > x z > y How can we extend this to more than 2 players?}+N aWorst - Case EquilibriaElias Koutsoupias and Christos Papadimitriou@"]QQ#  R+b m@iAn Efficient, Exact Algorithm for Solving Tree-Structured Graphical GamesLittman, Kearns, (Singh?)b@3||a  LVAL N::According to Cooper at al. they are symmetric games "which exhibit multiple Nash eqilibria which are Pareto-rankable" However, there is a footnote to Thomas Schelling, The Strategy of Conflict, which states that he used the term to refer to games in which the multiple Nash eq yielded identical payoffs. Also called "collaboration games." We will use the Pareto-optimal def and also make "collaboration games" available --------------------------------------- Agents have common payoffs or should coordinate to get their highest payoffs. In 2x2 games, have three equilibria: - two symmetric equilibria in pure strategies - one symmetric equilibrium in mixed strategies_+oNnnnnnnampleAppDocName346 |T00481P@sgRRRR%Y+idsAppwizSampleAppDocName345@F@j^RRRR/X*idsAppwizSampleAppDocName344 @^^RRRR'W'idsAppwizSampleAppDocName343|F03589|F03589 |T00478B@n`RRV'idsAppwizSampleAppDocName342|F03586|C02805 |T00483n`RRU)idsAppwizSampleAppDocName341p@^^RRRR'T(idsAppwizSampleAppDocName340 @^^RRRR'S'4idsAppwizSampleAppDocName339 |T00479@sgRRRR7 R&4idsAppwizSampleAppDocName338 |T00482P@sgRRRR% P$ idsAppwizSampleAppDocName336r@@j^RRRR/O# idsAppwizSampleAppDocName335@@j^RRRR'N" idsAppwizSampleAppDocName334@^^RRRR'M! idsAppwizSampleAppDocName333@@j^RRRR'L idsAppwizSampleAppDocName332|F03301|F03301 |T00411n`RRK idsAppwizSampleAppDocName3uThe Set of Nash Equilibria of a Supermodular Game Is a Complete LatticeO_Stability in Competition uSelection Criteria in Coordination Games: Some Experimental ResultsKuRationalizability, Learning, and Equilibrium in Games with Strategic Complementarities^_Potential Games_Multi-Agent Reinforcement Learning: Theoretical Framework and an AlgorithmR_Multi-Agent Influence Diagrams for Representing and Solving GamesI_Multi-Agent Algorithms for solving graphical games:uMonotone Comparative Strategies'uMixed Equilibria in Games of Strategic Complements are UnstableGuLocal-Effect GamesuGame Theory and Agents uGame Theory (II) uGame Theory (I)!uExistence of Nash Equilibrium in N-Person Games without QuasiconcavityN_Equilibrium in Hotelling's model of competition7 _Efficient Nash Computation in Large Population Games with Bounded InfluenceSuComputing Supergame Equilibria& _Computation of Equilibria in Finite Games1_Complexity Results about Nash Equilibria0 _Bounding the inefficiency of equilibria in nonatomic congestion gamesM#uAn Iterative Method of Solving a Game-uAn Experimental.[al$[game-reference].*= 3 #g 5@Bounding the inefficiency of equilibria in nonatomic congestion gamesT. Roughgarden and E. Tardos{{{] +N  nnn!nnn Assigned ReferencesLookup_assigned toz@cW3 Computing Supergame EquilibriaJudd, Yeltekin, ConklinCCC* ]+mNTT`````Feee!eee                               ! " #  $ & ' ( ) * + , - . / 0 1 2 3 % 4 6 7 8 9 : ; < = > ? @ A B  #  #  #  #  # # # # # # # # # # # # # #  #  #  # 5 # # # # # # # # ### #!#"###$#%#&#'#(#)#*#+#,#-#.##/#1#2#3#4#5#6#7#8#9#:#;#<#= #>#0#?#A#B#C#D((((((( ( ( (  (  ( (  ( #@(((((( ((((((((( ((((!("(#($(%(&('((()(*(+ (, (- (. (/ (0(1 (2( (3(5(6(7(8 $[game-reference].*= 3 # 4p@Efficient Nash Computation in Large Population Games with Bounded InfluenceM. Kearns and Y. Mansour}}}c  LVAL {&T7 y Q -  y [ A ) x [ =  h ;  r Z 6  xS+ qN0vY)pZero-Sum Games )Welfare Game0Weak Dispersion GamespWar of attrition6pUniform Local-Effect Game with clique-Uniform Local-Effect Game!!)Unbalanced Game#)Tree Structured Game)Traveler's Dilemma 0Symmetric Binary Global Games%pStag and Hare-)Soccer Game)Small Pig)Simplified Poker)Simple Point Catcher Game!)Simple Inspection Game 3Simple Ambush Game%)Shapley's Game0Selfish Dispersion Games pSecond price auctions formulated as strategic game:pSAT Games)Rock, Paper, ScissorspRoad GamepRing structured game()Random GamesPrisoner's DilemmapPotential Games0Partial Dispersion Games +)Parallel Network GamespN-Player Prisoner s Dilemma&)N-Player Chicken*)Network Games)Morra pModern Manufacturing)Modeller's Dilemma3Minimum Effort GamespMatching PenniespMajority VotingpLocation GamesLocal-Effect Games 3Linear Cournot DuopolypInspection Game))Hotellings Game)Hero pCollaboration games are a subset of coordination games. There is a footnote in Cooper et al. to Thomas Schelling, The Strategy of Conflict, which states that he used the term coordination games to refer to games in which the multiple Nash eq yielded identical payoffs, and also called these "collaboration games." Since we are using the less restrictive definition of coordination games, we will use collaboration games to refer to these coordination games with all Nash eq yielding equal payoffs.s+N  `````````````F&&&&&&&&* g tblStyles.PictureSizeMode8 g tblStyles.PictureTiling6 gtblStyles.PictureAlignment9 gtblStyles.PictureData4 gtblStyles.Picture0 g!tblSectionStyles.SectionStyleID> gtblSectionStyles.Section7 g tblSectionStyles.SpecialEffect= gtblSectionStyles.BackColor9 gtblSectionStyles.StyleID7 gtblSectionStyles111 tblStyles###  G G  GtblStylestblSectionStylesX@OC#  tblStyles.PictureType4 g tblStyles.PicturePaletteData; g tblStyles.RecordDividers7 g tblStyles.PictureSizeMode8 g tblStyles.PictureTiling6 gtblStyles.PictureAlignment9 gtblStyles.PictureData4 gtblStyles.Picture0 g!tblSectionStyles.SectionStyleID> gtblSectionStyles.Section7 g tblSectionStyles.SpecialEffect= guThe Set of Nash Equilibria of a Supermodular Game Is a Complete LatticeO_Stability in Competition uSelection Criteria in Coordination Games: Some Experimental ResultsKuRationalizability, Learning, and Equilibrium in Games with Strategic Complementarities^_Potential Games_Multi-Agent Reinforcement Learning: Theoretical Framework and an AlgorithmR_Multi-Agent Influence Diagrams for Representing and Solving GamesI_Multi-Agent Algorithms for solving graphical games:uMonotone Comparative Strategies'uMixed Equilibria in Games of Strategic Complements are UnstableGuLocal-Effect GamesuGame Theory and Agents uGame Theory (II) uGame Theory (I)!uExistence of Nash Equilibrium in N-Person Games without QuasiconcavityN_Equilibrium in Hotelling's model of competition7 _Efficient Nash Computation in Large Population Games with Bounded InfluenceSuComputing Supergame Equilibria& _Computation of Equilibria in Finite Games1_Complexity Results about Nash Equilibria0 _Bounding the inefficiency of equilibria in nonatomic congestion gamesM#uAn Iterative Method of Solving a Game-uAn Experimental.[al$[game-reference].*= 3 #game-refere #Existence of Nash Equilibrium in N-Person Games without QuasiconcavityNishimura, FriedmangggR d+tNTT`````````````````````````Fnnn#nnngguThe Set of Nash Equilibria of a Supermodular Game Is a Complete LatticeO_Stability in Competition uSelection Criteria in Coordination Games: Some Experimental ResultsKuRationalizability, Learning, and Equilibrium in Games with Strategic Complementarities^_Potential Games_Multi-Agent Reinforcement Learning: Theoretical Framework and an AlgorithmR_Multi-Agent Influence Diagrams for Representing and Solving GamesI_Multi-Agent Algorithms for solving graphical games:uMonotone Comparative Strategies'uMixed Equilibria in Games of Strategic Complements are UnstableGuLocal-Effect GamesuGame Theory and Agents uGame Theory (II) uGame Theory (I)!uExistence of Nash Equilibrium in N-Person Games without QuasiconcavityN_Equilibrium in Hotelling's model of competition7 _Efficient Nash Computation in Large Population Games with Bounded InfluenceSuComputing Supergame Equilibria& _Computation of Equilibria in Finite Games1_Complexity Results about Nash Equilibria0 _Bounding the inefficiency of equilibria in nonatomic congestion gamesM#uAn Iterative Method of Solving a Game-uAn Experimental.[al$[game-reference].*= 3 #game Monotone Comparative StrategiesMilgrom and ShannonMonotone Comparative StaticsMilgrom, Shannonspp^@@++ a+LPPPPP2R888S&WYkJUd8888+koLS'WYkJUd888B~WYkJUd888B+koL~WYkJUd888D~WYkJUd888D+koL~WYkJUd88>F~WYkJUd88>F+koL~WYkJUd88@F~WYkJUd88@F+koL~WYkJUd8::D~WYkJUd8::D+koL~ WYkJUd8@6~ WYkJUd8@6+koL~ WYkJUd:<<~ WYkJUd:<<+koL~ WYkJUd<@~WYkJUd>@+koL~WYkJUd>F6~WYkJUd>F6+koL~\J`dfdkmMJiO+W~\J`dfdkmMJiO+q~\d\ovd8868~\d\ovd8868+koL~\d\ovd886>~\d\ovd886>+koL~\d\ovd886@~\d\ovd886@+koL~\d\ovd8:68~\d\ovd8:68+koL~\d\ovd8:6B~\d\ovd8:6B+koL~\d\ovd8<68~ \d\ovd8<68+koL~!\d\ovd8<6B~"\d\ovd8<6B+koL~#\diQJbLYxSdi`~$\diQJbLYxSdi`+bdfiYbm~%\diQJbLYxSdi`+bdfiYbm+koL~&\diQJbLYxSdi`+koL~'\diQJbLYxSdi`:~(\diQJbLYxSdi`:+bdfiYbm~)\diQJbLYxSdi`:+bdfiYbm+koL~*\diQJbLYxSdi`:+koL~+\diQJbfdkmMJiO?bQsfdkmMJiO+W?bQsfdkmMJiO+q?bQufiQkk+k^Yf?bdi`J^fdkmMJiO+W?bdi`J^fdkmMJiO+q?diUfdkmMJiO+W?diUfdkmMJiO+WLW?diUfdkmMJiO+q?diUfdkmMJiO+qLW? diUfdkmMJiO+qLq? iQf^vfdkmMJiO+W? iQf^vfdkmMJiO+q? kJ\oiJfdkmMJiO+W? kJ\oiJfdkmMJiO+q?kQufiQkk+k^Yf?mMfdkmMJiO?vQufiQkk+k^Yf?vofJM\+k^Yf?OJmJJMMQkkfJUQkOJmJLJkQkSdi`k `dOo^QkiQ^JmYdbkWYfkiQfdimk kMiYfmkkvkiQ^mJL^QkJfsx+hivL^dM\Mdbmid^kJfsx+hivMdbmid^bJ`QkJfsx+hivOLmvfQYbOQuQkJfsx+hivOLmvfQfJbQkJfsx+hivOLmvfQhoQiYQkJfsx+hivOLmvfQiQ^JmYdbkJfsx+hivOLmvfQmJL^QkJfsx+hivSi`kmv^QkJfsx+hivfJbQL^dM\kJfsx+hivfJbQUidof^QqQ^kJfsx+hivifmkmv^QkJfsx+hivkJ`f^QOJmJJfsx+hivmJL^QSYQ^OkLYx+mL^Jim`Jfk LYx+mL^Mdbmid^^Ykm!LYx+mL^mQ`f^Ykm"Ls+mL^LmbJMmYdbk#Ls+mL^fYMmoiQk$Sisx+mL^JOdib`Qbmk%^LsYx+mL^JimS`kvkJMMQkkkmdiJUQ`kvkJMQk`kvkdL[QMmk`kvkhoQiYQk`kvkiQ^JmYdbkWYfk`m`+mL^JMmYdbJiUkS`m`+mL^JMmYdbkS`m`+mL^QqQbmJiUkS`m`+mL^^dd\ofkSfJkmQQiidikSfi+mL^JimSkL`+mL^MdOQSkL`+mL^kLSi`Mdbmid^kSksx+mL^UidofkS mL^JffkmiYbUkS mL^Mdbmid^fidfkS mL^Mdbmid^kS mL^OJmJLJkQmvfQSYQ^OkS mL^OJmJLJkQmvfQkSmL^OJmJLJkQmvfQmJL^QkSmL^SYQ^OkSmL^SYQ^OmvfQkSmL^Sdi`JmSmL^Uidof^QqQ^kSmL^YbOQuQkSmL^Ybfom`Jk\kSmL^fJbQL^dM\kSmL^fJbQfidfkSmL^fJbQkSmL^fidfQimYQkSmL^hoQiYQkS .[al Selection Criteria in Coordination Games: Some ExpCooper, DeJong, Forsynthe, RossSelection Criteria in Coordination Games: Some Experimental ResultsCooper, DeJong, Forsynthe, Rossall human subjects__>> I+N```````````````````````````````````````````Fnnn+nnn*          uThe Set of Nash Equilibria of a Supermodular Game Is a Complete LatticeO_Stability in Competition uSelection Criteria in Coordination Games: Some Experimental ResultsKuRationalizability, Learning, and Equilibrium in Games with Strategic Complementarities^_Potential Games_Multi-Agent Reinforcement Learning: Theoretical Framework and an AlgorithmR_Multi-Agent Influence Diagrams for Representing and Solving GamesI_Multi-Agent Algorithms for solving graphical games:uMonotone Comparative Strategies'uMixed Equilibria in Games of Strategic Complements are UnstableGuLocal-Effect GamesuGame Theory and Agents uGame Theory (II) uGame Theory (I)!uExistence of Nash Equilibrium in N-Person Games without QuasiconcavityN_Equilibrium in Hotelling's model of competition7 _Efficient Nash Computation in Large Population Games with Bounded InfluenceSuComputing Supergame Equilibria& _Computation of Equilibria in Finite Games1_Complexity Results about Nash Equilibria0 _Bounding the inefficiency of equilibria in nonatomic congestion gamesM#uAn Iterative Method of Solving a Game-uAn Experimental.[al$[game-reference].*= 3 #game-referencegame-referenceEE) />@ Stability in CompetitionH. Hotelling>>>0 @+PN`````````````````````````````````````````````````````````````````````````````Fnnn)nnn&&& & & & & && @@`uThe Set of Nash Equilibria of a Supermodular Game Is a Complete LatticeO_Stability in Competition uSelection Criteria in Coordination Games: Some Experimental ResultsKuRationalizability, Learning, and Equilibrium in Games with Strategic Complementarities^_Potential Games_Multi-Agent Reinforcement Learning: Theoretical Framework and an AlgorithmR_Multi-Agent Influence Diagrams for Representing and Solving GamesI_Multi-Agent Algorithms for solving graphical games:uMonotone Comparative Strategies'uMixed Equilibria in Games of Strategic Complements are UnstableGuLocal-Effect GamesuGame Theory and Agents uGame Theory (II) uGame Theory (I)!uExistence of Nash Equilibrium in N-Person Games without QuasiconcavityN_Equilibrium in Hotelling's model of competition7 _Efficient Nash Computation in Large Population Games with Bounded InfluenceSuComputing Supergame Equilibria& _Computation of Equilibria in Finite Games1_Complexity Results about Nash Equilibria0 _Bounding the inefficiency of equilibria in nonatomic congestion gamesM#uAn Iterative Method of Solving a Game-uAn Experimental.[al$[game-reference].*= 3 The Set of Nash Equilibria of a Supermodular GameLin ZhouThe Set of Nash Equilibria of a Supermodular Game Is a Complete LatticeLin ZhouGG== ea+qEI) / B p uThe Strategy of Conflict _Team Games As Models of Intergroup Conflicts4_Simulated annealing of games equilibria.1 uPure Nash Equilibria: Hard and Easy Games1_On the np-completeness of finding an optimal strategy in games with common payoffsZBOmniscience and Omnipotence: How they may Help - of Hurt - in a GameL_Nash propagation for Loopy Graphical Games2_Multi-Agent Reinforcement Learning: Theoretical Framework and an AlgorithmR"uIterative Solution of Games by Ficticious Play6 _Graphical Models for Game Theory( BGeometric Games and Their Applications. BGames of StrategyBFriend-or-Foe Q-learning in general-sum games.6_Equilibrium in Hotelling's model of competition7 _Efficient Nash Computation in Large Population Games with Bounded InfluenceSBDeception in 2 X 2 Games  _Bounding the inefficiency of equilib The Strategy of ConflictThomas Schellingbook Green BF637 .N4 S3 1980TT6$ 21111GNo Maybe Yes  LVAL, Give players some fixed choices for arms levels by parameterizing on upper and lower bounds of choices. Award payoffs based on the sum of two functions: - a negative cost function which is a function of your own level of arms, which must be smooth - a smooth, concave function which is a function of the difference between your own level and your opponent's LVAL )N,,̄ B BBB˵ ʵʵʵ@ @@@@@@@@@@@@@@@@ d ddddddddddddddɯ4R#B BB??2Wu@K Wu@tobeincluded9@~FFF:::::::8 @Rvr@vr@~sq_cGenerators~sq_cText189@4MR2KeepLocal TbVVVVVVT `QOvr@vr@~sq_cGenerators~sq_cgame-reference subform19y @4MR2KeepLocal Txxxxxxv `PTur@Ovr@~sq_cGenerators~sq_cgame-game subset subform9 @4MR2KeepLocal Tzzzzzzx `O tr@ur@~sq_cGenerators~sq_cgame-game subset subform19x @4MR2KeepLocal T||||||z `JG=wp@G=wp@Superset Query9@E}JJJ>>>>>>>< @IN0wp@_L=wp@Superset Query9?v@J}@bVVJ>>>>>>< `HTvp@Tvp@Subset Query9@.}FFF:::::::8 @Gvp@T wp@Subset Query9W;v@:@^RRF::::::8 `F`vp@Zvp@~sq_rgame-game subset96@4MR2KeepLocal TXLLLLLLJ `EZo@EZo@Sets of Games9@ HHH<<<<<<<: @g|Yo@l˹Xp@Generators9@`@"l|@ZNNB6666664 `#n@#n@Unassigned References9b@ XXXLLLLLLLJ @QÏn@gn@Unassigned References9-@A@K}|@NpddXLLLLLLJ `Fn@PFn@reference Query9{@@ |@ NdXXL@@@@@@> `saϗn@saϗn@~sq_rAll References InMR2OrientationOrderByOnNameMapDefaultViewColumnWidthColumnOrderColumnHiddenRequiredAllowZeroLengthDisplayControlIMEModeIMESentenceMode$UnicodeCompressionGUIDValidationRuleValidationText FilterOrderByDescription FormatInputMaskCaptionDefaultValue    Uqf;H8SSK Wu@tobeincludednC-qf;H8SSinclude ,M7c3grqf;H8SSid  qf;H8SSinclude       m       nC- "Maybe"I id     ,M7c3gr LVAL NHHi @@`@ @   @`According to Cooper at al. they are (symmetric) games "which exhibit multiple Nash eqilibria which are Pareto-rankable" However, there is a footnote to Thomas Schelling, The Strategy of Conflict, which states that he used the term to refer to games in which the multiple Nash eq yielded identical payoffs. Also called "collaboration games." We will use the Pareto-optimal def and also make "collaboration games" available --------------------------------------- Agents have common payoffs or should coordinate to get their highest payoffs. 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Personal34445569_ArgentinaVDB22   ,0000Cdigo Postal5564_ArgentinaH64,,   ,!(999) 0000-0000Nmero de telfono(206) 5543-4534_ArgentinanlNN*   0000PLZ4723Austria.  _  \(99999\)00099999Phone Number(29384)23487756AustriapbbDD, _  0000Postal Code4556_AustraliaD20((   (999) 000 0000Phone Number(55) 555 4333_AustralialZX>>&   !\(999) 9900\ 0000Phone Number(02) 9333 1234_AustraliavdbFF.  99999Extension63215_US620&&  00000-9999Zip Code98052-6399_USHDB..  000-00-0000Social Security Number531-86-7180_UShdbLL  !(999) 000-0000Phone Number(206) 555-1212_USb^\@@(  99\->L<LL\-00Medium DateMedium Date25473_WorldWiden\ZP:$  09:00 >LLMedium TimeMedium Time0.13333_WorldWidejXVH2  00:00Short TimeShort Time0.13333_Wuu_&u_$u_uu u___uu___uuuu"u _uu u u u!u uu A course in microeconomic theoryDavid M. KrepsA Course in Microeconomic TheoryDavid M. Krepsnnn^<<,, a+N      SQiQbMQK## )*, +[]^\!&'#$%"RTUS 7 = > 9 : ; < 8 ? D E F G H @ T | } ~         U    mputation of Equilibria for Extensive Two-Person GamesDaphne Koller, Nimrod Megiddo, Bernhard von Streferencegame-referencegame-referencereferenceidreferenceid{weO3/+'referencecategory-referencecategorcoMR2 GUIDNameMap ќLkvW  U_&kE-0Ygn@Assigned ReferencesV㛃H/ӯon_&kE-titlek&%^) Lѳeŷ_&kE-authors㩻'O-s_&kE-assignment detailszEIJۮ _&kE-in queueSFK0s z_&kE-assigned toM#MF./ԅyIn@įpeopletF,Kz1M#MF./ԅyname_QJe8r~UzM#MF./ԅyid9@N#__&kE-comment1^'"3HD E_&kE-uselessMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultVQ.[Assigned References].*G 3Q # Q6[Assigned References].titleO Q@ QAssn `.[al$[game-reference].*= 3 #game-referencegame-reference -h@Potential GamesD. Monderer and L.S. 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JohanssonGame Theory and AgentsStefan J. Johanssonppp[CC." A"+2Nmm`````F.[al$[game-reference An experimental study of N-person iterated prisoneR@X. Yao and P. DarwenAn Experimental Study of N-Person Iterated Prisoner's Dilemma GamesX. Yao, P. Darwen``J> a+*NSS```````Fwwwwwwwww~ww~ww~ww~ww}ww}ww}ww}ww}ww}ww}ww}ww}ww}ww}ww}ww}ww}ww}ww}ww}ww}ww}wwswwqwwqww ww wwo(]F ܈p݈ppwwwwwpppwppsppppppوpp܈pp}ppppppwppQppwppwwwwwwwwwwwwww~wwwwwwwwwwwwwwwwwwwwwww܈wwwxw戈wxw興sxwxx݈wwwwwwwwwwwwwwwwwwwwwwwww܈ws݈܈ws݈܈wsw݈܈݈爈ws.[al$[game-refer Rationalizability, Learning, and Equilibrium in GaMilgrom and RobertsRationalizability, Learning, and Equilibrium in Games with Strategic ComplementaritiesMilgrom, RobertsSS>> A1+ANJJ`````````FGGGGGLLL@@@@@@@> @ @B @Biz_tblControlList.V@RRRFFFFFFFD @1=@@Biz_tblArtmaps.? @JJJ>>>>>>>< @@@apwz_qryTableFields.@0@/`TTHHHHHHHF @O;@@apwz_qrySampleData.?@+@*^RRFFFFFFFD @׳@׳@apwz_qryRptStyles.@+|@*\PPDDDDDDDB @+@+@apwz_qryPaneGroupLevels.@&|@*h\\PPPPPPPN @M@M@apwz_qryPaneBlocks.@&|@%^RRFFFFFFFD @=i@r@apwz_qryFrmStyles.@&|@%\PPDDDDDDDB @@0E@apwz_qryDbTypeTables.@&@%bVVJJJJJJJH @`@@apwz_qryDbTypeRelations.a@$@%h\\PPPPPPPN @  @w<@apwz_qryDbTypeQueries.@$|@!dXXLLLLLLLJ @ W@@apwz_qryDbTypePanes.o@$@!`TTHHHHHHHF @ l@S@apwz_qryDbTypeIndexes.@ @!dXXLLLLLLLJ @ :@@apwz_qryControlNames.@ @bVVJJJJJJJH @ XF@XF@apwz_qryBlockControls. @@dXXLLLLLLLJ @w@w@USysRegInfo.@ DDD88888886 @}@}@DataAccessPages.@@@@@@@@@@> }@}@SysRel..........., }@}@Modules.0000000000. }@}@Scripts.0000000000. }@}@Reports.0000000000. }@}@Forms.,,,,,,,,,,*  }@}@UserDefined.A@DDD88888886 @ }@}@SummaryInfo.@\DDD88888886 @}@}@MSysAccessStorageSTGREL.PPPPPPPPPPN }@}@ MSysAccessStorage.DDDDDDDDDDB }@}@MSysRelationships/ DDDDDDDDDDB }@}@MSysQueries/ 88888888886 }@}@MSysACEs/ 22222222220 }@}@MSysObjects/ 88888888886 }@ˇ@MSys.[al$[game-reference].*= Mixed Equilibria in Games of Strategic ComplementsEchenique and EdlinMixed Equilibria in Games of Strategic Complements are UnstableEchenique, EdlinSS>> !LVALhD(pD( ?@ pD(pDpD pD4 !pDpDpDpDpDpDpDpD  d people.id peoplepeople.namepDpDpDpD pD.Zo@pDpD pDg$ pDg$ peoplepDXpDxpD8 pDpDk2Zo@1~sq_calgorithm~sq_cCombo7pD pDHpD pDPpDpDpDpDg$pDg$ people pDpD pDpDpDpD pD pDp pD pD8pD@pDHpDPpDXpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDpDxpD8pD pD pD8 pD`HpD8 pD pDz  pDpD pD0j$pD pD pDP pD pD d pD0 pD pD pD pD8 pD people pD8 pDPrimaryKeyidH pDpDv `pD8pDHpDpD pD pqD pD pD pD pD pD pD pD pD pD pD pD pD pD pD pD pD pD pD pD pD pD pD pD pD pD pD pD pDpDpDpDpD pD pDpeoplePrimaryKeypD pD`pD` pD`pDpD pDpDpDpDpD8 pD LVALNMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLReplicable  <       URAP)&,Kn@referenceSFK0s zRAP)&assigned tozEIJۮ RAP)&in queueV㛃H/ӯonRAP)&titlek&%^) LѳeŷRAP)&authors㩻'O-sRAP)&assignment details9@N#_RAP)&comment Os|NNI LVALND I(0 ? I(I(( I(I(k  0 for all x in [0,1]. A candidate attracts the votes of those citizens whose favorite positions are closer to his position than to the position of any other candidate; if k candidates choose the same position then each receives the fraction 1/k of the votes that the position attracts. The winner of the competition is the candidate who receives the most votes. Each person prefers to be the unique winning candidate than to tie for first place, prefers to tie for first place than to stay out of the competition, and prefers to stay out of the competition than to enter and lose."LVALNOOTwo player version from Hotelling's work: "The buyers of a commondity will be supposed uniformly distributed along a line of length l, which may be Main Street in a town or a transcontinental railroad. At distances a and b respectively from the two ends of this line are places of business A and B. Each buyer transports his purchases home at a cost c per unit distance. Without effect upon the generality of our conclusions we shall suppose that the cost of production to A and B is zero, and that unit quantity of the commodity is consumed in each unit of time in each unit of length of line." ----------------------------- Multiplayer version from a course in game theory: "Each of n people chooses whether or not to become a political candidate, and if so which position to take. There is a continuum of citizens, each of whom has a favorite position; the distribution of favorite positions is given by a density function f on [0, 1] with f(x) > 0 for all x in [0,1]. A candidate attracts the votes of those citizens whose favorite positions are closer to his position than to the position of any other candidate; if k candidates choose the same position then each receives the fraction 1/k of the votes that the position attracts. The winner of the competition is the candidate who receives the most votes. Each person prefers to be the unique winning candidate than to tie for first place, prefers to tie for first place than to stay out of the competition, and prefers to stay out of the competition than to enter and lose."]LVALmhDO >5  ? >5>5>5x>5x>5>5  >5>5>5>5>5>5>5>5  #GAMUT Games.gameidgame-reference-GAMUT Games.referenceidH>5@>5>5>5 >5/cž@>5>5>5&'>5&p4GAMUT Games>5>5>5 >5>5]n@W~sq_dGAMUT Games~sq_dgame-reference subform1>5 >5>5 >5>5>5>5 >5&->5&game-reference >5h>5 >5p>5>5>5>5>5>5__gameid>5 >5>5X >5 >58>5@>5H>5P>5X>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5x>5>5 >5 >5 >5 >5 >5 >5z  >5@>5 >5&>5 >5>5 >58 >5 >5 >50 >5 >5 >5 >5 >5game-referenceX >5p >5 >5 >5 >5referenceid-referencegame-referencePrimaryKey gameid#gamegame-reference >5>5v >5>5>5>5>5>q5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>5>50>5 >5@>5>5>5#>5game-reference>5x>5>5x>5>5H >5@>5x>5>5 x>5>5 0>58>5L>5PrimaryKey(>5d>5 >5[__gameid]>5`>5h>5>5>5 >5>5>5>5>5PrimaryKey@>5>5>5@>5>5@>5x>5 >5Nнs3sU% j h >  Z  P   D  z:ǘǘǘǘǘǘǘǘǘǘǘǘǘǘǘǘǘ @ @ @ @ @ @reference.title. g categorcategory!!! category!!! category!!! categorcategorcategory!!! category!!! category!!! categorcategorcategory!!! category.categoryid2 gcategory.categoryid2 g @do@do @do@do ' reference.t@do ' @do@do@do @do@do ' reference.t@do ' @do@do@do '@do ' @do ' @do@do@do@do '@do@do ' reference.title. 'reference.comment0 greference.[in queue]3 g reference.[assignment details]= greference.[assigned to]6 greference.authors0 greference.title. greference###  G G@co ' reference.title. 'reference.comment0 greference.[in queue]3 g reference.[assignment details]= greference.[assigned to]6 greference.authors0 greference.title. greference###  G G@bo ' reference.title. 'reference.comment0 greference.[in queue]3 g reference.[assignment details]= greference.[assigned to]6 greference.authors0 greference.title. greference###  G G@ao ' reference.title. 'reference.comment0 greference.[in queue]3 g reference.[assignment details]= greference.[assigned to]6 gLVAL{&T7 y Q -  y [ A ) x [ =  h ;  r Z 6  xS+ qN0vYLMMMMMFor the two player version, which is probably the more correct version to use: Parameterize on the length of the line l, the length a of the segment on the far side of A, the length b of the segment on the far side of B, and the transportation cost c. (a + b < l) if x is player 1's action and y is player 2's action then the payoff to player 1 is USUALLY: 0.5(l + a - b)x - (x^2)/2c + xy/2c and likewise the payoff to player 2 is USUALLY: 0.5(l - a - b)y - (y^2)/2c + xy/2 However, if y > x + c(l - a - b) then player 2 will get nothing and player 1 will get all (l * x), and likewise if x > y + c(l - a - b) then player 2 will get all (l * y) and player 1 will get nothing. (The paper has a minus sign instead of a plus here but that seems to be a typo) Might want to think about range of prices that players are allowed to choose in order to keep the game interesting ----------------------- Generate random set of positions which could be of arbitrary size. Generate a (random?) continuous density function for the distribution of citizens over these positions. We could parametrize the density function based on.. something. 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Inspection Game~@y@ Inspection Game@/#o Majority Voting@y@Majority Voting@/#Stag and HareStag and Hare$!Modern ManufacturingModern Manufacturing2Drilling for OilDrilling for Oil*Arms RacesArms Races5Diamond-Type Search ModelDiamond-Type Search Model<!!!!u4Supermodular Games2@ Supermodular Games:&&o3Bertrand Oligopoly@yBertrand Oligopoly:&&2Cournot Duopoly@yCournot Duopoly4##3$Location Games@yLocation Games2""#War of attritionWar of attrition*e"Second price auctions formulated as strategic gameSecond price auctions formulated as strategic gamen::::u!First price auctions formulated as strategic gamesFirst price auctions formulated as strategic gamesn::::Matching PenniesB@ @ Matching PenniesB0$N-Player Prisoner s Dilemma@@ N-Player Prisoner s DispectiInspection Game~@y@Inspection GameNN=1%%(4 LVALD Parameterize on n = number of players = number of actions. Generate a symmetric game in which the highest payoffs are at those outcomes in which all n players are playing different actions. Fill in all other payoffs ordered such that a more dispersed outcome with always have a higher payoff for all players than a less dispersed outcome. How dispersed an outcome is can be measured in different ways, for example by calculating entropy or calculating standard deviation. LVAL Parameterize on the functions to be used (can use one for each player for each facility, or one common function for all players for each facility) and the number of facilities available to choose from. Set up a mapping between action numbers and subsets of facilities chosen. At each outcome, calculate the number fo players who chose each facility. Assign payoffs to players as the sum over all facilities chosen by that player of the function for that player/facility given the number of players who chose the facility. LVAL Generate a matrix of payoffs for one player (common payoff so all others receive the same) where all of the highest payoffs occur on the diagonal (but the payoffs on the diagonal may not all be the same).. Notice this does not require the game to be symmetric, which is not always part of the definition --------------------------------------------------------------------------- For two players, can generate a payoff matrix a, w b, x c, y d, z such that a > c d > b w > x z > yRLVALbhDZ Y  ?YYYYYYU  YYYYYYYY  -GAMUT References.gameidgame-reference7GAMUT References.referenceidxYpYYY YE@Y8Y YH( YH(#GAMUT References0YYYH YY]n@a~sq_cGAMUT References~sq_cgame-reference subform28Y YY YYYYYH( YH(game-reference YY YYYYYYY__idY YY Y Y8Y@YHYPYXYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYxYY Y YH Y YH Y Yz  Y`Y Y(8Y YY Y` Y Y Y0 Y Y Y YH Ygame-reference Y Y Y Y Yreferenceid-referencegame-referencePrimaryKey gameid#gamegame-reference YYv 0YY YYYqYYYYYYYYYYYYYYYYYYYYYYYYYYYYYPY Y`Y8YY#Ygame-referenceYYYY0Yp YhYYY Y@Y XY`YtYreferenceid(YY Y [__id]YYYYY YYYYYreferenceidhYYY`YY`YYH Yv LVAL Parameterize on the inverse demand function P and the two cost functions C1 and C2. If Ci is a cost function for player i and P is the inverse demand function, then for each outcome, if each player j chooses action yj then the payoff for player i is P(y1+y2)yi - Ci(yi). ----- Could also parameterize on the number of players to make the game extensible, but really it is only studied in the two player case so we will limit it to that. LVALMR2ODBCTimeoutMaxRecordsRecordLocksRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL <       UKH[^ URAP)&\o@_referenceV㛃H/ӯonRAP)&titlek&%^) LѳeŷRAP)&authors Ϧj#ΟΟΟΟ΁c ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘__gameid!!!*  G*  G**  G**  G**  G* **  G**  G*  G*  G**  G**  G* *  G**  G* **  G* **  G* **  G*  G*  G**  G**  G**  G*  G*  G**  G*  G* **  G* **  G*  G*  G**  G*  G* **  G* **  G*  G*  G**  G*  G* **  G* **  G*  G*  G**  G**  G*  G*  G**  G*  G* *  G* **  G*  G*  G*  game-ga game-ga game-game s game-game subset11 game-game subset111  game-game subset111  game-game subset111 game-game subset111 game-game subset111  game-game subset111  game-game subset111  game-game subset11 game-game subset111 [game-game subset].childid9 g[game-game subset].parentid: g   G game-game subset111 [game-game subset].childid9 g[game-game subset].parentid: g   G G  G, LVAL< {&c2 | W / m W 9   w V 9  e F  s P 8  wV1 pO,oT7)pZero-Sum Games )Welfare Game0Weak Dispersion GamespWar of attrition6pUniform Local-Effect Game with clique-Uniform Local-Effect Game!!)Unbalanced Game#)Tree Structured Game)Traveler's Dilemma 0Symmetric Binary Global Games%pStag and Hare-)Soccer Game)Small Pig)Simplified Poker)Simple Point Catcher Game!)Simple Inspection Game 3Simple Ambush Game%)Shapley's Game0Selfish Dispersion Games pSecond price auctions formulated as strategic game:pSAT Games)Rock, Paper, ScissorspRoad GamepRing structured game()Random GamesPrisoner's DilemmapPotential Games0Partial Dispersion Games +)Parallel Network GamespN-Player Prisoner s Dilemma&)N-Player Chicken*)Network Games)Morra pModern Manufacturing)Modeller's Dilemma3Minimum Effort GamespMatching PenniespMajority VotingpLocation GamesLocal-Effect Games 3Linear Cournot DuopolypInspection Game))Hotellings Game)Hero pHawk and Dove,)Grid Game)Greedy Game0,0 5,4 4,5 4,5 0,0 5,4 5,4 4,5 0,0 This game has a unique equilibrium point [(1/3,1/3,1/3),(1/3,1/3,1/3)] yielding the exectation (3,3). Yet, any deviation by a player, followed by a best reply, yields BOTH players more than (3,3). --- When I google this, the results I find mainly seem to say that Shapley's Game is a modifed Rock, Paper, Scissors: 0,0 1,0 0,1 0,1 0,0 1,0 1,0 0,1 0,0 We should get a precise def.LVALhD _[  ?x_[ _[8_[_[_[_[U  _[ _[_[_[_[_[_[ _[  7GAMUT References.algorithmid%algorithm-reference7GAMUT References.referenceid_[_[_[ _[ (_[<@(_[P_[ 0Y_[H(1Y _[H(YGAMUT ReferencesX_[_[0_[p _[(_[E n@i~sq_cGAMUT References~sq_calgorithm-reference subformP_[ _[_[ _[_[_[_[ _[H(7 _[H(algorithm-reference _[_[ _[_[_[_[_[_[_[__id_[ _[_[ _[ (_[8_[@_[H_[P_[X_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[8_[_[x_[0_[ _[ _[p _[ _[p _[ _[z  _[_[H _[ (P_[ _[(_[8 _[ _[ _[8 _[0 _[ _[ _[8 _[p _[%algorithm-reference _[ _[_[ _[8_[referenceid7referencealgorithm-referencePrimaryKeyalgorithmid7algorithmalgorithm-reference_[_[v _[p_[_[_[_[_q[_[_[_[_[_[_[_[_[_[_[_[_[_[_[_[_[_[_[_[_[_[_[_[_[_[_[_[_[_[ 8_[_[_[_[-(_[algorithm-reference_[_[_[_[_[ _[_[_[_[ _[_[ _[_[_[referenceid( _[_[ _[ [__id]$_[_[_[_[D_[ (_[l_[@_[H_[0_[referenceid_[_[_[_[x_[_[_[p _[ LVALMR2ODBCTimeoutMaxRecordsRecordLocksRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL <       UKH[^ URAP)&\o@_referenceV㛃H/ӯonRAP)&titlek&%^) LѳeŷRAP)&authors LVALhD o]T ?o]o] o]po]i $o]o]o]$o]Lo]|o]o]o] o]$o]o]o]o]8o]ho]o]o]o]$o]o]o]o]o]o]o]o]o]$o]o]o]$o]Lo]|o]o]o] o]                 reference.titlereferencereference.bibtexreference.id!reference.authors)reference.assigned to7reference.assignment details#reference.in queue!reference.useless!reference.commento]  o] o]xo]  o] @o]o] o]Q( o]Q( o]Q( $o]Q( Lo]Q( |o]Q( o]Q( o]Q(  o]Q(referencex o]   o]` o]Xo] o]\o@)~sq_fGAMUT Referenceso] o]o] o]o] o]o] o]o] 8o]o] ho]o] o]o] o]o] o]o]o]o]o]o]8o]ho]o]o]o] o]Q( O\\o]Q(\o]Q(\$o]Q(O\Lo]Q(ePi|o]Q(Keo]Q(O\\o]Q(pO\\ o]Q(pO\reference o]P o] o]X o] o]` o] $o]h o] Lo]p o] |o]x o] o] o] o] o] o] o]o]o]o]o]8o]ho]o]o]o] o]o]o] o]8o]`o]o]o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o] o]o]ho]o]o] Ho]Xo] o]Xo] $o]Xo]`Ho]Xo] o]Xo] Ho]Xo]  o]Xo] o]Xo]  o]Xo]  $o]z `o]o]xo]8S(o]`o] o]po]o]o]o]o]@o]o]xo]o]o]o]o]o]  o]o] `o] o]o] o]@o] xo]o]o]  o]L$o]o] o](o]0o]8o]@o]Ho]Po]`o]o]o]o]@o]xo]o]o] o]Xo]reference o]o]o] titlePrimaryKeyido]o]v o]o]o]o]o]oq]o]o]o]o]o]o]o]o]o]o]o]o]o]o]o]o]o]o]o]o]o]o]o]o]o]o]o]o]po] o]o]Xo]o]po]referencePrimaryKeyo]po]o]o]o]o]o]o]Ho]o]o]Xo]uP. X7  z S 1  l K , 4pWeak Equilibrium3pUnique Equilibrium(pSymmetric Games pSupermodular Games2pStrict Equilibrium&pSeparable Games1pPure-strategy equilibrium!%pPolymatrix Games0pPerfect Information/pPerfect Equilibria Exist .pPareto ordered / Strictly Better Equilibria Exist9$pNon-Braithwaite Games-pNo pure-strategy Nash when N > 3(,pNo Pure-Strategy Equilibria##pMixed-Motive Games!pImproper Braithwaite Games"+pImperfect Equilibria pGraphical Games*pDominated Strategies Removed$pDominant Strategy7pConstant-Sum GamespComplete OppositionpCompact Representation8pCommon-Payoff Games"pClassical Matrix " f@ Dominant Strategies for All== Lp @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @xyz{|}~ 33334$4$4$4$4$4$5$5$ 5$5$ 5$ 5$7$7$7$7$7$F FFF F F FF GG;GG?G@GAGBGCG DG EGIFIbIcIdI^I_I`IaI eI fIGKnKrKpKqKsKoLtLxLvLwLyLuMzM~M|M}M{NNNNYYYYYYZZZZZddhdidjdkdldmdndodqd pdnrnvntnunwnsoxo|ozo{o}oyp~pԂpԀpԁpԃpqԄqԈqԆqԇqԅrԉrԍrԋrԌrԊtԣtԧtԥtԦtԤvԭvԱvԯv԰vԮwԲwԶwԴwԵw Էw ԸwԳxԹxԽxԻxԼx ԾxԺ  !childidgame-game subsetch  !referenceidgame-referencereferenceidgame-reference subform1.referenceidbL00  !gameidgame-referencegamei@@Centipede Game<<, j LVAL Paramatrize size with time. Can easily make a payoff matrix where optons are discrerte times and the player decides ahead of time during which time slot he will go for the dollar. Payoffs are a whenever players picks an earlier time slot than opponent, b whenever player picks a later time slot than opponent, and c whenever both pick the same time slot, with a > b > c. LVAL N<<This description doesn't quite meet the game as it is generally pictured, but gives an idea of context: "There is a pile of pounds on the table. X and Y take it in turns to take either one or two coins from the pile, and they keep the coins they take. However, as soon as either of them takes two coins, the game stops, and teh rest of the coins are cleared away. So long as they each take only one coin when their turn comes, the game continues till the pile is exhausted." "Standard backwards-induction argument concludes that X will take two coins at her first move, thereby ending the game." Including this game in our generator because it can be treated as a timing game where each player chooses on which move he will take two coins if given the chance up front. LVAL Associate a number with each action. (Can be 1, 2, 3, . . .) For each outcome, calculate two-thirds the average of the actions chosen by each player and figure out which players have guessed closest to this. Give some payoff amount to the player who has the closest guess (or split this amount between multiple players if there is a tie) and give all other players 0.LVAL h hTTTT@ ------------------------------------------------------ More broad definiGenerate a payoff matrix for one player (common payoff so all others will be receive the same payoffs) with the highest payoffs down the diagonal all of equal value.Generate a payoff matrix for one player (common payoff so all others will be receive the same payoffs) with the highest payoffs down the diagonal all of equal value. Notice this does not require the game to be symmetric which is not always part of the definition.To generate a payoff matrix from a potential function, start by picking one strategy profile S, and calling its payoff v. Then take x = P(S) - P(S') for every other strategy profile S' that differs from S in only one action, and the gain from deviating from S to S' is -x. Now do all S'' that differ from S' in only one action, and so on until you have explored every strategy profile. Incidentally, note that all strategy profiles that maximize P are (pure strategy) Nash.Pick any SAT formula and follow the paper. Set of strategies for both players is Union(L,V,C,{f}), where L is the set of literals, V - vars, C -clauses, f - a special default action The payoff matrix contains entries 1,-2,+2, 2-n, and payoff(f,f)=0 If SAT assignment exists, there is a symmetric NE, with payoff of 1 for both, and uniform distribution over satisfying _literals_ otherwise, (f,f) is a NE with 0 payoff.Parameterize on maximum number of turns the players can take if they do not choose to stop. If X stops the game before Y and does it on his nth turn, he gets 2n-1 and Y gets 2n-2. If Y stops the game before X and does it on her nth turn, she gets 2n+1 and X gets 2n-2. If the game continues until the end, the player whose move ends the game on their nth turn gets 1 less than they would have by stopping the game that turn, and the other player gets 1 (or 3?) more than they would have. The final payoffs if the game continues forever seem to vary among different descriptions.t@ +@Guess 2/3 of the average@@&illingDrilling for Oil@= @>Drilling for OilPP>2&&`,N,,,,Y Y Y Y  Y  Y qdPLIDSLIDOriginalFontIDMappedFontIDMultiplierCommentsqDqDq DqDqDq DqqDqDq DqYYYLocFontIDPrimaryKeyUSFontID "nu6JKr :U"OriginalFontID    Original font is mainly US font, but when a new style is added "OriginalFontID" is the same as "MappedFontID" -   0   mMappedFontID   B :Mapping font from the US font   0   mMultiplier    In case the localizer changed the size of the font (US Size * Multiplier)   1   mbComments x       m  [PLID      0   m[SLID      0   mMR26OrderByOn"DatasheetFontName&DatasheetFontHeight&DatasheetFontWeight&DatasheetFontItalic,DatasheetFontUnderlineTabularCharSetTabularFamilyOrientation$DatasheetForeColorNameMapColumnWidthColumnOrderColumnHiddenRequiredAllowZeroLengthDisplayControl$UnicodeCompressionGUID   Arial      "     U ZjjM9 FontID      bFontName         m bComments  &       m MR2ODBCTimeoutMaxRecordsOrderOnOrderByOnSccStatusReplicableGUIDRecordLocksRecordsetType FilterOrderByOrientationNameMapDOLE <   P84V      UŜP84VPՋ@tblSectionStylesǜP84VŜP84VStyleIDi^'`BYU,@؈htblStylesɜP84VŜP84VBackColorʜP84VŜP84VSpecialEffectȜP84VŜP84VSectionƜP84VŜP84VSectionStyleIDi^'`Bi^'`BPicturei^'`Bi^'`BPictureDatai^'`Bi^'`BPictureAlignmenti^'`Bi^'`BPictureTilingi^'`Bi^'`BPictureSizeModei^'`Bi^'`BRecordDividersi^'`Bi^'`BPicturePalett@!Ordinally Symmetric Games99LVALW,wHDfUZ H!?`fUfUfUfU < fU`fUfUfUfUfU@fUxfUfUfU0fU0fU0fU0fU0fU fU`fUfUfUfU         'Generators.game.namegame5Generators.game.description/Generators.game.generate/Generators.game.included=Generators.game.coding completeXfUPfUfU0fU(fUQ.x@hfUfU PfU`fU  fUx|a `fUx|a fUx|a fUx|a fUx|aGeneratorsfU  fUhfUfU(fUS|-x@game8 fU   fU( fUhfUfU8L)x@coding queuefU `fUfU fUfU fUfU fUfU  fU`fUGenerators.name`fU+Generators.descriptionfU%Generators.generatefU%Generators.includedfU7Generators.[coding complete] fU fU`fUid fUx|aa `fUx|a fUx|a fUx|ah fUx|at gameGenerators`fU  fU fU ( fU fU X fUP fU fUx fU  fU fU`fUgame.namefUgame.descriptionfUgame.generatefUgame.included fU+game.[coding complete] fUx|a `fUx|a fUx|a fUx|a fUx|a game  fU@fU 2 fUHfU b fUPfU fUXfU hfU`fU`fUfUfUfU fUcoding complete fUfUfU (fU8fUPfUhfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfU(fUfUhfU fUhfU $fUhfU $PfUhfU  PfUhfU fUz fUpfUfUxa`fUPfU fUfU fUfUfUfU0fUfU PfU fU fUfU0fU<hfUpfUxfUfUfUPfUfUfUfU0fUhfUgame fU fU 8fU#PfUtobeincludedgamePrimaryKeypeoplegame gameidhfUfUv hfUXfUG0fUfUfqUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfUfU fU8fUfUfUgamefUfU PfUfU PfUfU PfUfUhfUfUfUHfUfUXfUfUhfUfUfUfUfU fU&%game.[is generator] fUfUfUfUxfUfU fUfUfUfUfUtobeincludedgame (fU fUa;,fUfU<fU 0fUdfU8fU@fU fU fUfU8fUfU hfUfU @ fUfU PfUfU8fUpfUpfUfULVALИ~"^ NЄ ̈́̈́̈́̈́̈́̈́̈́̈́̈́̈́̈́̈́̈́̈́̈́̈́̈́̈́̈́̈́̈́̈́ O55555sq_fgame-refer[MR2ODBCTimeoutMaxRecordsRecordLocksRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL <       My]NaνK0 ( U|욳[J7j1QS|-x@GeneratorsL~Jޘ)9g|욳[J7j1Qincludedq9g0MCҜ|욳[J7j1Qname{|N@٠Ym|욳[J7j1QdescriptionUE]=,J&ZbN|욳[J7j1QgenerateMR2ANSI Query ModeAccessVersion BuildProjVerHasCustomGroupsAppTitleStartUpForm&StartUpShowDBWindow(StartUpShowStatusBarStartUpMenuBar$AllowShortcutMenusAllowFullMenus(AllowBuiltInToolbars&AllowToolbarChanges AllowSpecialKeysAppIcon,StartupShortcutMenuBar&UseAppIconForFrmRpt.Use Default Page Folder0HaveSetDefaultPageFolder   08.50                 MR2 GUIDNameMap d J۩c1  UnGsM U\"[p@S game-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childid'ςO>;{;x@S gameq9g0MCҜ'ςO>;{name!hdRI3 'ςO>;{gameidi J N''ςO>;{is generatorMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLReplicable  <     &  U'ςO>;{;x@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byL~Jޘ)9g'ςO>;{included ^2”eIG`<}sMR2 GUIDNameMapX m㛷ZBa&Generators.included? 3&Generators.generate? 3,Generators.descriptionE 3Generators.name7 3Generators!!! 6pfUfUhfU LVAL Original model is for two players and is cts: Really this is infinite extensive form - NF might blow up :( We have consumers drawn uniformly from [0,1] interval. We have two firms Each firm first chooses location on [0,1] The locations x_1 and x_2 are then observed. They really only consider G(x_1, x_2) - so locations need not count as actions. Then each firm gets to charge the price p_i Consumers minimize distance+cost when choosing the firm, so this determines payoff - see paper for details. LVAL Parameterize with a graph and functions. Label each node and each edge of the graph with a function. For each outcome, figure out how many players have chosen each node (where each node represents an action). For each player, calculate the payoff function as the sum of the node function of the action he has chosen evaluated on the number of players who chose this node, and all edge functions for edges leading into this node evaluated on the number of players who chose each neighboring node.t LVAL ά(?0reference LVAL~"^ N8866666666 6 6 6 6 6 6 666MR2ODBCTimeoutMaxRecordsRecordLocksRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL <       My]NaνKx p U|욳[J7j1QS|-x@GeneratorsL~Jޘ)9g|욳[J7j1Qincludedq9g0MCҜ|욳[J7j1Qname{|N@٠Ym|욳[J7j1QdescriptionUE]=,J&ZbN|욳[J7j1Qgenerateŗ`AjD&*,|욳[J7j1Qcoding complete LVAL N//Generate n player version of game with m candidates. Can assign each of the n voters a utility for each candidate winning, and create n dimensional matrix where each player has m choices and utility is for each player is based on their utility rating of the candidate with the most votes. No necessary restrictions on player utilities for each candidate. Can be parameterized based on both number of voters and number of candidates.v LVAL {&c2 | W / m W 9   u P /  n Z >  g L )  mP/ uI(lH-)pZero-Sum Games )Welfare Game0Weak Dispersion GamespWar of attrition6pUniform Local-Effect Game with clique-Uniform Local-Effect Game!!)Unbalanced Game#)Tree Structured Game)Traveler's Dilemma 0Symmetric Binary Global Games%pStag and Hare-)Soccer Game)Small Pig)Simplified Poker)Simple Point Catcher Game!)Simple Inspection Game 3Simple Ambush Game%)Shapley's Game0Selfish Dispersion Games pSecond price auctions formulated as strategic game:pSAT Games)Rock, Paper, ScissorspRoad GamepRing structured game()Random GamesPrisoner's DilemmapPotential Games0Partial Dispersion Games +)Parallel Network GamespN-Player Prisoner s Dilemma&)N-Player Chicken*)Network Games)Morra pModern Manufacturing)Modeller's Dilemma3Minimum Effort GamespMatching PenniespMajority VotingpLocation GamesLocal-Effect Games 3Linear Cournot DuopolypInspection Game))Hotellings Game)Hero pHawk and Dove0Guess 2/3 of the average ,)Grid Game)Greedy GamepGrab the Dollar7)FriendspFirst price auctiFor two-finger morra, generate 2-player 4 by 4 payoff matrix given as (note this is zero sum so player 2's payoffs can be obtained by subtracting these from 0): 0 c -b 0 -c 0 0 b b 0 0 -a 0 -b a 0 a > b > c > 0 (in book, a = 4, b = 3, c = 2) Could probably be extended (three finger morra? More players?) but nobody seems to have been interested in extensions.6+F{tmf_XQJC<5.'  xqjc\UNG@92+$BBBBB __________________ _ _ _ _ _________&u% ?Web Page for course "Rationality, Democracy and Public Policy" at colorado.eduhttp://sobek.colorado.edu/~mciverj/4224_res.html@ZZ  (LVAL8Pick a graph to represent a network topology. For each link pick a function representing delay (function of the traffic). Set of pure strategies for each agent is the set of paths from source to destination. Payoff = - delay. LVAL Players have two actions called C and N. Parameterize on the number of players who must contribute (i.e. choose action C) in order for all to get reward. Payoffs for each player are as follows: C and k-2 or less others choose C: -c C and k-1 others choose C: b-c C and k or more others choose C: b-c N and k-2 or less choose C: 0 N and k-1 choose C: 0 N and k or more choose C: bHf @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @YYYYZZZZZnrnvntnunwnsoxo|ozo{o}oyp~pԂpԀpԁpԃpqԄqԈqԆqԇqԅrԉrԍrԋrԌrԊtԣtԧtԥtԦtԤyyyyyȄ4(4,4*4+4-4)4.424041434/494;4<4:4Q4U4S4T4R !%#$&"'+)*(,0./-MQOPRNSWUVXTY][\^Zimklnjosqrtpuywxzv          --------IIIIIIIIIIIIIIIIIIIIIIIIIIII LVAL {&c2 | W / m W 9   u P /  n Z >  g L )  mP/ uI(lH-)pZero-Sum Games )Welfare Game0Weak Dispersion GamespWar of attrition6pUniform Local-Effect Game with clique-Uniform Local-Effect Game!!)Unbalanced Game#)Tree Structured Game)Traveler's Dilemma 0Symmetric Binary Global Games%pStag and Hare-)Soccer Game)Small Pig)Simplified Poker)Simple Point Catcher Game!)Simple Inspection Game 3Simple Ambush Game%)Shapley's Game0Selfish Dispersion Games pSecond price auctions formulated as strategic game:pSAT Games)Rock, Paper, ScissorspRoad GamepRing structured game()Random GamesPrisoner's DilemmapPotential Games0Partial Dispersion Games +)Parallel Network GamespN-Player Prisoner s Dilemma&)N-Player Chicken*)Network Games)Morra pModern Manufacturing)Modeller's Dilemma3Minimum Effort GamespMatching PenniespMajority VotingpLocation GamesLocal-Effect Games 3Linear Cournot DuopolypInspection Game))Hotellings Game)Hero pHawk and DoveLet C(i) be the payoff if you cooperate and i others cooperate, and let D(i) be the payoff if you defect while i others cooperate. This is considered a PD if 1) D(i) > C(i) for 0 <= i <= n-1 2) D(i+1) > D(i) and also C(i+1) > C(i) for 0 <= i < n-1 3) C(i) > (D(i) + C(i-1)) / 2 for 0 < i <= n-1 in order to make sure these properties hold, can parameterize on three function parameters X, Y, and Z, and use functions C(i) = Xc + Y D(i) = Xc + Z where 0 < Z - Y < X alternately, can generate as a compound game@!@>Ring structured gameBB, z+ 'Differential GamesAvner FriedmanJ@ ":..  G+WpJ}, e ( C r D c < _Weighted Majority Games Have Many mu-Values3_Values of Smooth Non-Atomic Games: The Method of Multilinear Approximation in The Shapley ValueguThe Strategy of Conflict _The Complexity of two-person zero-sum games in extensive form.F_Team Games As Models of Intergroup Conflicts4&uSufficiency Conditions for Nash Equilibrium in N-Person Differential GamesR$uSome Topics in Two-Person Games'_Simulated annealing of games equilibria.1 uPure Nash Equilibria: Hard and Easy Games1_On the np-completeness of finding an optimal strategy in games with common payoffsZBOmniscience and Omnipotence: How they may Help - of Hurt - in a GameL_Nash propagation for Loopy Graphical Games2_Multi-Agent Reinforcement Learning: Theoretical Framework and an AlgorithmR"uIterative Solution of Games by Ficticious Play6 _Graphical Models for Game Theory(_Equilibrium in Hotelling's model of competition7 _Efficient Nash Computation in Large Population Games with Bounded InfluenceS_Efficient Computation of Equilibria for Extensive Two-Person GamesJDynamic Noncooperative Game Theory*%uDifferential GamesBDeception in 2 X 2 Games  _Bounding the inefficiency of equilibria in nonatomic congestion gamesMA Tax )Dynamic Noncooperative Game TheoryBasar, Tamer, Olsder@ "PDD.  b+r &Some Topics in Two-Person GamesLloyd ShapleyAnnals of Mathematical Studies (1964) too basicxa:+ + Bd@ Weighted Majority Games Have Many mu-ValuesMonderer@wYMMC  {&c2 | W / m W 9   u P /  n Z >  g L )  mP/ uI(lH-)pZero-Sum Games )Welfare Game0Weak Dispersion GamespWar of attrition6pUniform Local-Effect Game with clique-Uniform Local-Effect Game!!)Unbalanced Game#)Tree Structured Game)Traveler's Dilemma 0Symmetric Binary Global Games%pStag and Hare-)Soccer Game)Small Pig)Simplified Poker)Simple Point Catcher Game!)Simple Inspection Game 3Simple Ambush Game%)Shapley's Game0Selfish Dispersion Games pSecond price auctions formulated as strategic game:pSAT Games)Rock, Paper, ScissorspRoad GamepRing structured game()Random GamesPrisoner's DilemmapPotential Games0Partial Dispersion Games +)Parallel Network GamespN-Player Prisoner s Dilemma&)N-Player Chicken*)Network Games)Morra pModern Manufacturing)Modeller's Dilemma3Minimum Effort GamespMatching PenniespMajority VotingpLocation GamesLocal-Effect Games 3Linear Cournot DuopolypInspection Game))Hotellings Game)Hero pHawk and Dove0Guess 2/3 of the average ,)Grid Game)Greedy GamepGrab the Dollar7)FriendspFirst price auctions formulated as strategic games:")Exponential Game pDrilling for Oil)Dispersion Games)Discoordination Games pDiamond-Type Search Model! 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Also called "Iterated Dominance Equilibrium"LVALqL' ^1 z \ 3 u T *  `  | ] ;  { a 0 3300)Weakly Dominant StrategDefined only on 2x2 games Games in which one player can make a unilateral shift from the "natural outcome" which will effectively force the other player to shift as well in repeated games in order to avoid a low payoff. The "natural outcome" is defined using the following assumptions: 1. If both players have a dominant strategy, both will use it 2. If only one player has a dominant strategy, he will choose it, and the other will choose the strategy which maximizes his payoff under the assuption that the first player has chosen his dominant strategy 3. If the game has a single Pareto eq, the players will choose the strategy which contains it 4. If neither player has a dominating strategy, and if the game has either no pareto eq or more than one, each player will choose the stragy which contains his maximin outcome (i.e. the strategy which avoids the smallest of the four payoffs) TODO: identify and label subsets LVAL  @ @ @ @ @ @ @ @ @ @ @ @ @ @ @)&)')1)2)))) )))))))))) )#)$)()*)50000 0 00333 3 3 ppppppppp p p pppppppp p%p(p)p,p.p1p3p4p5p6p7p8p9p<)) )))))")%)))+)/)0)3)4)6)70 3 3p p ppp+p2p:p;)))) ) )))!0ppppp!p"p#p$p&p-p-p-p-p-p-MR2S;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up S9 R 8 R ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up R 9 Q 8 Q ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up Q 9 P 8 P ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up P 9 O 8 O ;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up O 9 28 2;$ o`zzi '\?Rbw_x6mXVra*NH.sɥh9wt1!{ƿa\r{Ua@ڲ>v9W up 29 N 8 N ;$ o`zzi '\?R"A geometric game is a game having the following form: Two antagonists, known hereafter as RED and BLUE, choose subsets R and B respectively of a set S. BLUE then receives from RED a payoff which is a function of the triple R, B, and R (intersection) B. The payoff need not be monetary, and for our purposes can be considered merely a score which BLUE wishes to maximize and RED wishes to minimize. . . . In general, RED and BLUE may not choose any subset of S, but rather RED must select from a collection R of admissible pure strategies for RED and BLUE from a collection B. . . . The term 'geometric' is described by specifying S, R, B, and the payoff." There are quite a few more games of various detail and extensibility described in this reference. LVAL qL' ^1 z \ 3 u T *  `  | ] ;  { a 0 ! U9%~~`C"?!jL.yZ+ rJ%kN,z 3(,pNo Pure-Strategy Equilibria#9pNo dominant strategies3Neutrally Stable Strategies##pMixed-Motive Games3)k-Bounded Treewidth Games!/)k-Bounded Neighbourhood4)k-Bounded Hypertree-width!Timing games in which the reward goes to the player whose move ends the game. The term preemption game seems to have different meanings in the literature. For example, in "A Taxonomy of 2x2 Games" it is used to mean games with two Pareto equilibria, for example Chicken. This is not the meaning we want to use for it though, as the timing game definition seems more naturally "preemptive."LVALqL' ^1 z \ 3 u T *  `  | ] ;  { a 0 vCCCCC)Weakly Dominant StDefined only on 2x2 games Games in which the player receiving a lower-than-optimal payoff in the "natural outcome" can shift unilaterally to a lower payoff which may result in the other player shifting as well if the game is repeated. The "natural outcome" is defined using the following assumptions: 1. If both players have a dominant strategy, both will use it 2. If only one player has a dominant strategy, he will choose it, and the other will choose the strategy which maximizes his payoff under the assuption that the first player has chosen his dominant strategy 3. If the game has a single Pareto eq, the players will choose the strategy which contains it 4. If neither player has a dominating strategy, and if the game has either no pareto eq or more than one, each player will choose the stragy which contains his maximin outcome (i.e. the strategy which avoids the smallest of the four payoffs) TODO: Identify and label subsetsLVALИ ```FFF z Pick number of p"Global games are games of incomplete information whose type space is determined by the players each observing a noisy signal of the underlying state. With strategic complementarities, global games often have a unique dominance solvable equilibrium, allowing a"Global games are games of incomplete information whose type space is determined by the players each observing a noisy signal of the underlying state. With strategic complementarities, global games often have a unique dominance solvable equilibrium, allowing analysis of a number of economic models of coordinatioon failure." The players each receive a different signal.Pick number of players and actions, fill the matrix with random numbers drawn from some distribution Used as a benchmark too often to omit.Games that are based on choosing a time to act. Choosing a time can be thought of as happening in advance, as nothing that players would learn over that time period could help them.(-2^b, 2^b+1) (0,0) (0,0) (2,-1) Interesting in repeated setting Needs exponential size DFS for NE strategies, but poly-size counting FA"At each play, Ruth and Charlie simultaneously extend either one finger or two fingers and call out a number. The player whose call equals the total number of extended fingers wins that many pennies from the opponent. In the event that neither players' call matches the total, no money changes hands." Four by four matrix of choices for each player. In the finger story, choose a pair of numbers representing the number of fingers you hold out and the number of fingers you think there will be total. Choices are (1, 2), (1, 3), (2, 3), and (2, 4) Can also do three finger, four finger, etc.Two prisoners are caught and asked to confess. Each prisoner chooses to cooperate or defect. Defect is the dominant strategy for both players and thus forms an equilibrium, even though it is the only pure out come which is not Pareto optimal. Extensible version listed under N-Player prisoners' dilemma.LVAL  u Y F (  i J   g &  l P 1 Can discretize on prices they cgenerate only one function per node, store at all outgoing edges -- or can store at node and have a different function to calculate the payoffThis is still incomplete: Given n players, and m actions. Let n_i(a) = #players choosing action i set payoff_i(a_i, a_{-i}) = -n_{a_i} * alpha (i.e. you incur delay according to the number of players using the same link). This is very similar to dispersion game.Discretize amounts that can be bid. Assign each player a valuation for winning the auction. At each outcome, the payoff to the player whose bid/action is the highest is (his valuation - the second highest bid) and the payoff to all other players is 0.Discretize amounts that can be bid. Assign each player a valuation for winning the auction. At each outcome, the payoff to the player whose bid/action is the highest is (his valuation - his bid) and the payoff to all other players is 0.Discretize time into some finite number of times steps equal to the number of actions. Generate random valuations v1 and v2 for each of the two players and random payoff units for each player which are subtracted from the players' utilities at each time step.Generate as other LEGs, but with only one function per node stored at all outgoing edges (or can store at node and have a different function to calculate the payoff).Generate a game in which all players have the same actions available. Set the highest payoffs for each player to be on the outcomes in which they are sharing their action with the fewest other agents. Set the payoffs of all other outcomes to be lower whenever there is less dispersion. Dispersion can be measure using entropy, standard deviation, or some other reasonable method.Parameterize on n and m and k. "Blue" agent gets to choose a function from the numbers {1,2,...,n} to the numbers {1,2,...,m}. "Red" agent gets to choose any subset of {1,2,...,n} with no more than k values. Payoffs as defined in the description.vLVALqL' ^1 z \ 3 u T *  `  | ] ;  { a 0 )Weakly Dominant Strategies"4pWeak Equilibrium3pUnique Equilibrium+pTrembling Hand Perfect Equilibria Exist/5)Tractable Pure-Strategy Equilibria* )Timing Game:pThreat-Vulnerable Games)Symmetric Games (weak sense)$(pSymmetric Games (strong sense)& pSupermodular Games2pStrict Equilibrium0)Small NeighbourhoodSignalling Games&pSeparable Games1pPure-strategy equilibrium!8pPure Coordination)Preemption Games%pPolymatrix Games.pPareto ordered / Strictly Better Equilibria Exist9 0Ordinally Symmetric Games!$pNon-Braithwaite Games-pNo pure-strategy Nash when N > 3(,pNo Pure-Strategy Equilibria#9pNo dominant strategies3Neutrally Stable Strategies##pMixed-Motive Games3)k-Bounded Treewidth Games!/)k-Bounded Neighbourhood4)k-Bounded Hypertree-width!6)Intersection of bounded treewidth and small neighbourhoodA!pImproper Braithwaite Games" pGraphical GamesGlobal Games)Geometric Games;pForce-Vulnerable Games)Evolutionarily Stable Strategies(pDominant Strategies for All#)Dominance-Solvable Equilibrium&7pConstant-Sum Games)Equilibrium is robust against slight perturbations in the players' *strategies* Other variations on the typical Nash are listed in the first chapter of the Evolutionary Game Theory book.LVAL,N11 `  | ] ;  { a 0 MR2.ValidationRuleValidationTextOrientation FilterOrderByOrderByOnNameMapDefaultViewGUIDColumnWidthColumnOrderColumnHiddenDescription FormatInputMaskCaptionDefaultValueRequiredAllowZeroLengthDisplayControlIMEModeIMESentenceMode$UnicodeCompressionDecimalPlaces    U'ςO>;{8L)x@gameq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byi J N''ςO>;{is generatorУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete  'ςO>;{$ game.name DESCdescription            {|N@٠Ym("extensible-action       Yes/No  j  NߜpZv  Nogenerate            UE]=,J&ZbNQ gameid       !hdRI3 name  M       m    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^+ ^+ ^+ ^+ ^+game-referenceX ^+p ^+ ^+ ^+ ^+referenceid-referencegame-referencePrimaryKey gameid#gamegame-reference ^+^+v ^+^+^+^+^+^q+^+^+^+^+^+^+^+^+^+^+^+^+^+^+^+^+^+^+^+^+^+^+^+^+^+^+^+^+0^+ ^+@^+^+^+#^+game-reference^+x^+^+x^+^+H ^+@^+x^+^+ x^+^+ 0^+8^+L^+PrimaryKey(^+d^+ ^+[__gameid]^+`^+h^+^+^+ ^+^+^+^+^+PrimaryKey@^+^+^+@^+^+@^+x^+ ^+ LVALhDV,X ? ,,X,0 ,V !,,,,,,,,  d tobeincluded.idtobeincluded'tobeincluded.include(, ,,, ,X,뾛@,,,8r%),8r%tobeincluded,,, ,,0IXu@7~sq_cGAMUT Games~sq_cCombo26, ,, ,,,,,8r%y gm,8r%gatobeincluded ,H, ,P,,, ,H, , ,8,@,H,P,X,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,X,,x,, , , ,`H, , ,z @ ,H,` ,t%, ,X , , , dX ,0( ,0 , ,X , ,tobeincluded , ,PrimaryKeyid ,,v ,,,,H,Hq,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,8, X,H, ,,0 ,tobeincludedPrimaryKey,0 ,, ,,,H,H,,H,, , LVALhD0,00X ?H ,0,, ,4 !,,,,,,,,  d people.id peoplepeople.name,,,, ,Ï뾛@,, ,^* ,^*people,`,,@ ,,k2Zo@7~sq_cGAMUT Games~sq_cCombo18, ,P, ,X,,,,^* ,^* people ,, ,,,, , ,x , ,8,@,H,P,X,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,x,@, , ,@ ,`H,@ , ,z  ,, ,a*, , ,X , , d ,0 , , , ,@ , people( ,@ ,PrimaryKeyidP ,,v h,@,P,, , q, , , , , , , , , , , , , , , , , , , , , , , , , , , , ,, ,,,(, ,peoplePrimaryKey, ,h,h ,h,, ,,,,,@ , LVALMR2 GUIDNameMap ZĹ2A)^[> z U^2”eIG`<}sBkx@Sets of Gamesq9g0MCҜ^2”eIG`<}sname{|N@٠Ym^2”eIG`<}sdescription NߜpZv^2”eIG`<}sextensible-actioni J N'^2”eIG`<}sis generatorѴa|F5AL^2”eIG`<}sentered byM#MF./ԅyk2Zo@Xd hpeople_QJe8r~UzM#MF./ԅyidtF,Kz1M#MF./ԅynameL~Jޘ)9g^2”eIG`<}sincludedqf;H8SS0IXu@Xd htobeincluded ,M7c3grqf;H8SSidnC-qf;H8SSinclude...B.,v\U\o@ 0game-reference subform1|C@a3-]n@4=game-referenceeSUnFJ ⩛|C@a3-gameid!hdRI3 ^2”eIG`<}sgameidd J۩c1%+՘@ 0game-game subset subform1nGsM U\"[p@(game-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childid\DE4ѽ3#՘@ 0game-game subset subform LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLReplicable  <     &  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byL~Jޘ)9g'ςO>;{included ^2”eIG`<}sK[!4 ,".(2 ,".(6koproperty-reference 8B@: !<G )<joP >property-reference 8B@B "<G )<jo@ B >property-reference$@ D'iH]]property-reference'J J L 8B@:NX|PHH P!RA@N0o( *Attribute VB_Name = "Form_refere@nce" Bas0{5387A37E-5987-4147-8737-2F7CD294CC17} |GlobaBlSpacFalse dCre atablTru PredecdlaId"E`xpose_TemplateDerivCus`tomizD$Option Codmp@ DT Sub Curt() On Erro@r GoTo_  If ChildIsOpen() Then Filter 1_Exit: " A rrMsgBoxH$Resu~AEndA6ToggleLink_Clic>kO7Mb8C!/CllH:4AF ρH.IfA1%L/MNPRMsP?Me.NewRecord~GFgs![property- F].Entr~y?MC'`""[ id] & @[e].# ]= q0FI!9!DoCmd.! " &XNot0]gMe![ RGOm ac,?xFuncC-JF`C!5(Sys`&(acGetObjectSt@O,:) A|ac.) <> Ja 8PRa#5 @_Dim stDocBAs SngNCri@ia (?c׶EJLabel4m Text5m Text6f Line7fLine8fLine9FormFooter,WDT=n#080:<=Babc$e g hijj,kBUvp@(0zuHJyPr U^OSCBv)VU@, !sti AᩰDn.Descri4 cHDL, 0 p  0   0   0 0BlobDelta2BlobDeltaPropData PropData 5P0E#*bel FormFooter coding priorityLabel ELECT priority.ID, priority.Fiel08w=Babce g hij1kQL[coding queue query].[coding complete]kSuu@m㛷ZByW, UgL۪H4nja”u@coding queue queryq9g0MCҜgL۪H4nname{|N@٠YmgL۪H4ndescriptionUE]=,J&ZbNPropData# 6D'1 UdŖ,__SRP_2Aq __SRP_3aV0  L.@Xޗ^8  U'ςO>;{RYn@defgjmnopdmdmdjdmdfdjdmm>;{extensiblegamͬazp2sDp4MReportHeaderdLabel8PageHeaderSectionDetailmnameddeghijklm9 LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLReplicable  <     &  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byL~Jޘ)9g'ςO>;{included ^2”eIG`<}s LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLReplicable  <     &  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byL~Jޘ)9g'ςO>;{included ^2”eIG`<}s LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLReplicable  <     &  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byL~Jޘ)9g'ςO>;{included ^2”eIG`<}s LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLReplicable  <     &  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byL~Jޘ)9g'ςO>;{included ^2”eIG`<}s LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLReplicable  <     &  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byL~Jޘ)9g'ςO>;{included ^2”eIG`<}s LVAL ЪΪΪΪΪΪΪΪΪΪΪΪΪΪΪΪΪΪW = a w 5 n nnnnnnnnnnɅMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL9  <      |욳[J7j1Q  U'ςO>;{Z6\o@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensibleUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL9  <      |욳[J7j1Q  U'ςO>;{Z6\o@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensibleUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byMR2 GUIDNameMap "G `AWr j U;ՊDO/ E n@algorithm-reference@] բr@<4o ARAP)&idMR2ValidationRuleValidationTextOrientation FilterOrderByOrderByOnNameMapDefaultViewGUIDColumnWidthColumnOrderColumnHiddenDescription FormatDecimalPlacesInputMaskCaptionDefaultValueRequiredDisplayControl     U~;rt <-LsQo];MR2 GUIDNameMap "G `AWr j U;ՊDO/ E n@algorithm-reference@] բr@<4o ARAP)&idMR2ValidationRuleValidationTextOrientation FilterOrderByOrderByOnNameMapDefaultViewGUIDColumnWidthColumnOrderColumnHiddenDescription FormatDecimalPlacesInputMaskCaptionDefaultValueRequiredDisplayControl     UOIkDJ[؁MR2 GUIDNameMap "G `AWr j U;ՊDO/ E n@algorithm-reference@] բr@<4o ARAP)&id LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLReplicable  <     &  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byL~Jޘ)9g'ςO>;{included ^2”eIG`<}s LVALMR2 GUIDNameMap ZĹ2A)^[>  U^2”eIG`<}sBkx@Sets of Gamesq9g0MCҜ^2”eIG`<}sName{|N@٠Ym^2”eIG`<}sDescriptioni J N'^2”eIG`<}sis generator NߜpZv^2”eIG`<}sextensible-action...B.,v\U\o@G` 0game-reference subform1|C@a3-]n@game-referenceeSUnFJ ⩛|C@a3-gameid!hdRI3 ^2”eIG`<}sgameidd J۩c1%+՘@ 0game-game subset subform1nGsM U\"[p@0Xgame-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childid\DE4ѽ3#՘@ 0game-game subset subform LVAL N  @MR2 GUIDNameMap d J۩c1  UnGsM U\ Zo@l0 Lgame-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childid'ςO>;{Z6\o@l0 Hgameq9g0MCҜ'ςO>;{name!hdRI3 'ςO>;{gameidi J N''ςO>;{is generatorMR2 GUIDNameMap d J۩c1  UnGsM U\ Zo@l0 Lgame-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childid'ςO>;{Z6\o@l0 Hgameq9g0MCҜ'ςO>;{name!hdRI3 'ςO>;{gameidi J N''ςO>;{is generatorMR2 GUIDNameMap \DE4ѽ3  UnGsM U\ Zo@ 0 Lgame-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childid'ςO>;{Z6\o@ 0 HgamMR2 GUIDNameMap d J۩c1  UnGsM U\ Zo@l0 Lgame-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childid'ςO>;{Z6\o@l0 Hgameq9g0MCҜ'ςO>;{name!hdRI3 'ςO>;{gameidi J N''ςO>;{is generatorMR2 GUIDNameMap \DE4ѽ3  UnGsM U\ Zo@ 0 Lgame-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childid'ςO>;{Z6\o@ 0 Hgameq9g0MCҜ'ςO>;{name!hdRI3 'ςO>;{gameidi J N''ςO>;{is generatorMR2 GUIDNameMap ...B.,v\h ` U|C@a3-]n@game-referenceoNڽF5߾d|C@a3-referenceidRAP)&\o@1 HreferenceV㛃H/ӯonRAMR2 GUIDNameMap d J۩c1  UnGsM U\ Zo@l0 Lgame-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childid'ςO>;{Z6\o@l0 Hgameq9g0MCҜ'ςO>;{name!hdRI3 'ςO>;{gameidi J N''ςO>;{is generatorMR2 GUIDNameMap d J۩c1  UnGsM U\ Zo@l0 Lgame-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childid'ςO>;{Z6\o@l0 Hgameq9g0MCҜ'ςO>;{name!hdRI3 'ςO>;{gameidi J N''ςO>;{is generatorMR2 GUIDNameMap ...B.,v\h ` U|C@a3-]n@game-referenceoNڽF5߾d|C@a3-referenceidRAP)&\o@1 HreferenceV㛃H/ӯonRAP)&titlek&%^) LѳeŷRAP)&authorsmr*˅O<>4o ARAP)&id LVALMR2 GUIDNameMap qi N:Sf ^ URAP)&\o@referenceV㛃H/ӯonRAP)&titlev2R{pI6#uRAP)&bibtexk&%^) LѳeŷRAP)&authorszEIJۮ RAP)&in queue9@N#_RAP)&comment1^'"3HD ERAP)&uselessSFK0s zRAP)&assigned toM#MF./ԅyk2Zo@x hpeopletF,Kz1M#MF./ԅyname_QJe8r~UzM#MF./ԅyid^2 'J>'f\o@ 0algorithm-reference subform;ՊDO/ E n@4Aalgorithm-reference@] բr@<4o ARAP)&id9bBgxWݘ՘@ 0game-reference subform2|C@a3-]n@game-referenceoNڽF5߾d|C@a3-referenceid LVALMR2 GUIDNameMap  qi N:S  URAP)&\o@referenceV㛃H/ӯonRAP)&Titlev2R{pI6#uRAP)&Bibtexk&%^) LѳeŷRAP)&Authors^2 'J>'f\o@P 0algorithm-reference subform;ՊDO/ E n@4algorithm-reference@] բr@<4o ARAP)&id9bBgxWݘ՘@ 0game-reference subform2|C@a3-]n@4game-referenceoNڽF5߾d|C@a3-referenceid LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding completeLVALV[fhDN\X ?N\N\ N\hN\\e <N\N\N\*N\JN\bN\N\N\N\N\N\N\N\ N\@N\XN\xN\N\N\N\N\N\N\N\N\N\N\N\N\N\N\N"\N\*N\JN\bN\N\N\N\N\                 game.namegamegame.description+game.extensible-actiongame.generategame.gameidgame.entered by!game.is generator+game.extensible-playergame.included'game.coding completeN\  N\ N\N\ N\S|-x@N\N\\$ N\($*N\($N\($*N\($JN\($]!bN\($deN\($ncN\($amN\($udN\($* game N\    N\ N\N\ N\͗՘@GeneratorsN\ N\N\ N\N\ N\N\ N\N\ @N\ N\  N\0 N\ 8 N\` N\ h N\ N\ N\ N\  N\ N\N\N\/game.[extensible-action]N\ N\@N\!game.[entered by] N\%game.[is generator]8 N\/game.[extensible-player]h N\N\+game.[coding complete] N\ N\($N:N\($N\($N*N\($JN\($ bN\($ N\($ N\($ N\($ N\($ game N\ N\ N\ N\ N\ N\ *N\ N\ JN\ N\ bN\ N\ N\ N\ N\ N\ N\ N\ N\ N\N\N\N\ N\@N\ N\8 N\h N\N\ N\ N\N\N\ N\8N\`N\N\N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\ N\N\xN\N\pN\ HN\N\ N\N\ $N\N\ N\N\ $N\N\`N\N\  N\N\  N\N\  N\N\  N\N\ N\z N\hN\(N\P$N\N\ N\N\(N\N\ `N\ N\N\0N\N\@N\N\PN\@N\`N\xN\pN\N\N\ N\ N\(N\ `N\N\N\N\@N\xN\N\P(N\N\N\N\N\N\N\N\N\N\N\N\(N\`N\N\N\N\@N\xN\N\N\game xN\N\ N\#N\tobeincludedgamePrimaryKeypeoplegame gameidN\N\v N\N\0\eN\N\Nq\N\N\N\N\N\N\N\N\N\N\N\N\N\N\N\N\N\N\N\N\N\N\N\N\N\N\N\N\N\ N\0N\N\hN\gameHN\hN\ N\hN\ N\hN\N\N\ N\N\XN\N\N\N\ N\N\  N\&%game.[i LVALs generator] $N\LN\N\N\N\N\hN\HN\ N\XN\ @ HN\N\ N\N\0N\XN\hN\N\hN\N\N\ LVALЪb ^  h # T  @ q,]p pppppp < <} " eFƕwD** ** DoCmd.Close acForm, "|P00329" End Sub Private Sub Report_Open (Cancel As Integer) DoCmd.OpenForm "|P00329", , , , , acDialog, "|P00330"MR2 GUIDNameMapb b8+mOvC]> 6 URAP)&,Kn@referenceV㛃H/ӯonRAP)&titlev2R{pI6#uRAP)&bibtexk&%^) LѳeŷRAP)&authorszEIJۮ RAP)&in queue9@N#_RAP)&comment1^MR2 GUIDNameMap ŴO$#  U^2”eIG`<}s>hYo@Sets of Gamesq9g0MCҜ^2”eIG`<}sname{|N@٠Ym^2”eIG`<}sdescription NߜpZv^2”eIG`<}sextensiblei J N'^2”eIG`<}sis generatorѴa|F5AL^2”eIG`<}sentered byM#MF./ԅyk2Zo@p2 4people_QJe8r~UzM#MF./ԅyidtF,Kz1M#MF./ԅyname...B.,v\U\o@,0game-reference subform1|C@a3-]n@ @game-referenceeSUnFJ ⩛|C@a3-gameid!hdRI3 ^2”eIG`<}sgameidd J۩c1W.\o@,0game-game subset subform1nGsM U\ Zo@@2 game-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childid\DE4ѽ3m '\o@,0game-game subset subformMR2 GUIDNameMap ќLkvW  U_&kE-0Ygn@Assigned ReferencesV㛃H/ӯon_&kE-titlek&%^) Lѳeŷ_&kE-authors㩻'O-s_&kE-assignment detailszEIJۮ _&kE-in queueSFK0s z_&kE-assigned toM#MF./ԅyk2Zo@0 4peopletF,Kz1M#MF./ԅyname_QJe8r~UzM#MF./ԅyid9@N#__&kE-comment1^'"3HD E_&kE-uselessMR2RecordLocksODBCTimeoutMaxRecordsRecoMR2 GUIDNameMap ќLkvW  U_&kE-0Ygn@Assigned ReferencesV㛃H/ӯon_&kE-titlek&%^) Lѳeŷ_&kE-authors㩻'O-s_&kE-assignment detailszEIJۮ _&kE-in queueSFK0s z_&kE-assigned toM#MF./ԅyk2Zo@0 4peopletF,Kz1M#MF./ԅyname_QJe8r~UzM#MF./ԅyid9@N#__&kE-comment1^'"3HD E_&kE-useless LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete LVAL.nnnnnnnnnnnnnnnnnnnnnnnnnnnnnn R2 GUIDNameMap b8+mOvC]f ^ URAP)&\o@referenceV㛃H/ӯonRAP)&tiMR2 GUIDNameMap d J۩c1  UnGsM U\"[p@n|MR2 GUIDNameMapL <$0JHXޗ^8(   U'ςO>;{*[o@gameq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{descriptionUE]=,J&ZbN'ςO>;{generate NߜpZv'ςO>;{extensibleMR2 GUIDNameMap d J۩c1  UnGsM U\"[p@n|game-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childid'ςO>;{?.Wu@nxgameq9g0MCҜ'ςO>;{name!hdRI3 'ςO>;{gameidi J N''ςO>;{is generatorMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLReplicable  <       URAP)&\o@referenceSFK0s zRAP)&assigned tozMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLReplicable  <       URAP)&\o@referenceSFK0s zRAP)&assigned tozEIJۮ RAP)&in queueV㛃H/ӯonRAP)&titlek&%^) LѳeŷRAP)&authors㩻'O-sRAP)&assignment details9@N#_RAP)&comment Os|NNIMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLReplicable  <       URAP)&\o@referenceSFK0s zRAP)&assigned tozEIJۮ RAP)&in queueV㛃H/ӯonRAP)&titlek&%^) LѳeŷRAP)&authors㩻'O-sRAP)&assignment details9@N#_RAP)&comment Os|NNIMR2 GUIDNameMapN JOKm * " UW#TH?h?gen@References Assigned to EugeneV㛃H/ӯonW#TH?h?titlek&%^) LѳeŷW#TH?h?authors㩻'O-sW#TH?h?assignment detailsMR2 GUIDNameMapn ^2 'J>'J B U;ՊDO/ E n@algorithm-reference~?ZH;ާwkS;ՊDO/ algorithmid+_I9$ @PfCDU@Nk2Zo@@2 algorithmܹT@Avb  ? >b>b>b>b>b>b  >b>b>b>b>b>b>b>b  -GAMUT Generators.gameidgame-reference7GAMUT Generators.referenceidx>bp>b>b>b >bI@>b8>b >b($`1`>b($$GAMUT Generators0>b>b>bP >b>b]n@a~sq_cGAMUT Generators~sq_cgame-reference subform18>b >b>b >b>b>b>b >b($->b($game-reference >b>b >b>b>b>b>b>b>b__gameid>b >b>b >b >b8>b@>bH>bP>bX>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>bx>b>b >b >bP >b >bP >b >bz  >bp>b >b$8>b >b>b >bh >b >b >b0 >b >b >b >bP >bgame-reference >b >b >b >b >breferenceid-referencegame-referencePrimaryKey gameid#gamegame-reference(>b>bv 8>b>b0>b>b>b>qb>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b>b`>b >bp>bH>b>b#>bgame-reference>b>b>b>b8>bx >bp>b>b>b >bH>b `>bh>b|>bPrimaryKey(>b>b >b[__gameid]>b>b>b>b>b >b>b>b>b>bPrimaryKeyp>b>b>bp>b >bp>b>bP >b LVALhD`b ? bb`b8 bV !bbbbbbbb  d tobeincluded.idtobeincluded'tobeincluded.include0b(bbb bJ@bbe(bb($>b)b($tobeincludedbbb bb0IXu@A~sq_cGAMUT Generators~sq_cCombo31b bb bbbbb($erb($imrtobeincluded bPb bXbbb bPb b b8b@bHbPbXb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bb`bbxbb b b b`Hb b bz H bPbh b$b( b` b b( b d` b00 b8 b( b` b btobeincluded b bPrimaryKeyid bbv bbbbPbPqbPbPbPbPbPbPbPbPbPbPbPbPbPbPbPbPbPbPbPbPbPbPbPbPbPbPbPbPb@b `bPb(bb8 btobeincludedPrimaryKeyb8 bb bbbPbPbbPbb b LVALhD8>cK8 ?P >c8>c>c >c4  >c>c>c>c>c>c>c>c d  people.name peoplepeople.id>c>c>c>c >cJ@>c>c>c($>c($people>ch>c>cH >c>ck2Zo@?~sq_cGAMUT Generators~sq_cText18>c >cX>c >c`>c>c>c >c($bb>c($people >c>c >c>c>c>c >c >c >c >c8>c@>cH>cP>cX>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>c>cx>cH>c >c H>cH >c >cH >c`>cz  >c>c >c$>c >c >c` >c d >c >c0 >c >c >c >cH >c people0 >cH >cPrimaryKeyidX >c>cv p>cH>cX>c>c >c >qc >c >c >c >c >c >c >c >c >c >c >c >c >c >c >c >c >c >c >c >c >c >c >c >c >c >c >c >c>c >c>c>c0>c >cpeoplePrimaryKey>c >cp>cp >cp>c>c >c>c>c>c>cH >c LVALMR2 GUIDNameMap&  L6D5͆  U|욳[J7j1QS|-x@Generatorsq9g0MCҜ|욳[J7j1Qname{|N@٠Ym|욳[J7j1Qdescription NߜpZv|욳[J7j1Qextensible-actionUE]=,J&ZbN|욳[J7j1Qgeneratei J N'|욳[J7j1Qis generatorѴa|F5AL|욳[J7j1Qentered byM#MF./ԅyk2Zo@0ChpeopletF,Kz1M#MF./ԅyname_QJe8r~UzM#MF./ԅyidУAљz@ܗ|욳[J7j1Qextensible-playerL~Jޘ)9g|욳[J7j1Qincludedqf;H8SS0IXu@0Chtobeincluded ,M7c3grqf;H8SSidnC-qf;H8SSinclude...B.,v\U\o@ 0game-reference subform1|C@a3-]n@ @game-referenceeSUnFJ ⩛|C@a3-gameid!hdRI3 |욳[J7j1Qgameid\DE4ѽ3#՘@ 0game-game subset subformnGsM U\"[p@0g(game-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childidd J۩c1%+՘@ 0game-game subset subform1 LVALΟ܍ ̄ B BBB L LLLm Ȇ  ǩƩƩƩƩƩƩDDDDDmĽvYo@oYo@~sq_cgame-6[o@[o@~sq_cgame-property Subform1~sq_cgameid9Y#4MR2KeepLocal Tznnnnnnl `'$P-6[o5b\o@#\o@~sq_cgame-reference subform2~sq_cgameid9j@n4MR2KeepLocal T|ppppppn `-6[o@[o@~sq_cgame-property Subform1~sq_cgameid9Y#4MR2KeepLocal6 e\o@e\o@Admin*********** 5 6W\o@ 6W\o@~sq_cgame-reference subform2~sq_cgameid9p@p4MR2KeepLocal T|ppppppn `-6[o@[o@~sq_cgame-property Subform1~sq_cgameid9Y#4MR2KeepLocal Tznnnnnnl `'$P[o@(Q[o@~sq_cgame-category Subform1~sq_cgameid9h@Q4MR2KeepLocal Tznnnnnnl `EZo@EZo@Sets of Games9@gHHH<<<<<<<: @g|Yo@-Yo@Generators9h @b)@a|@ZNNB6666664 ` n@wzn@~sq_freference9&@j4MR2KeepLocal TJ>>>>>>< ` n@ n@~sq_crefeά@ L.ualgorithmalgorithm4-referencereference:gamegame<8algorithm-referencealgorithm-reference9~game-referencegame-reference Clpeoplepeople LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding completeLVALi![whDd ?dd dhd\e <ddd*dJdbdddddddd d@dXdxddddddddddddddd"dd*dJdbddddd                 game.namegamegame.description+game.extensible-actiongame.generategame.gameidgame.entered by!game.is generator+game.extensible-playergame.included'game.coding completed  d dd dS|-x@ddN\d($NNd($0d($N\*d($N\Jd($J@bd($q_d($ Gd($ord($Te d($ game d    d dd d͗՘@Generatorsd dd dd dd dd @d d  d0 d 8 d` d h d d d d  d ddd/game.[extensible-action]d d@d!game.[entered by] d%game.[is generator]8 d/game.[extensible-player]h dd+game.[coding complete] d d($N\\d($N\\d($N\\*d($N\\Jd($N\\bd($N\\d($N\d($ d($N\d($am Hgame d d d d d d *d d Jd d bd d d d d d d d d dddd d@d d8 dh dd d ddd d8d`dddd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd dd ddxddpd Hdd dd $dd dd $dd`dd  dd  dd  dd  dd dz dhd(dP$dd dd(dd `d dd0dd@ddPd@d`dxdpddd d d(d `dddd@dxddP(dddddddddddd(d`dddd@dxdddgame xdd d#dtobeincludedgamePrimaryKeypeoplegame gameidddv dd0\eddqdddddddddddddddddddddddddddddd d0ddhdgameHdhd dhd dhddd ddXdddd dd  drLVAL @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ xyz{|}~ 33334$4$4$4$4$4$5$5$ 5$5$ 5D: |~  ?||||||  ||||||||  'Sets of Games.gameidgame-reference1Sets of Games.referenceid`|X||| |"pu@|(||H+|HSets of Games|||8 ||]n@[~sq_cSets of Games~sq_cgame-reference subform1(| || |||| |H-|Hgame-reference || ||||||@|__gameid| ||p | |8|@|H|P|X|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||x|| | P|8 | P|8 | |z  |@| |!(| || |P | | |0 | | | |8 |game-referenceh | | | | |referenceid-referencegame-referencePrimaryKey gameid#gamegame-reference||v ||||||q||||||||||||||||||||||||||||0||@| ||#|game-referenceP||P|||` |P||| |(| @|H|X|PrimaryKey |l| |[__gameid]|h|p||| |||||PrimaryKeyP|P||@||@|x|8 |LVAL &%game.[is generator] $dLdddddhdHd dXd @ Hdd dd0dXdhddhddd LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete LVALMZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZMR2 GUIDNameMapf "L K0TB : U|욳[J7j1Ql˹Xp@Generatorsq9g0MCҜMR2ANSI Query ModeAccessVersion BuildProjVerHasCustomGroupsAppTitleStartUpForm&StartUpShowDBWindow(StartUpShowStatusBarStartUpMenuBar$AllowShortcutMenusAllowFullMenus(AllowBuiltInToolbars&AllowToolbarChanMR2ANSI Query ModeAccessVersion BuildProjVerHasCustomGroupsAppTitleStartUpForm&StartUpShowDBWindow(StartUpShowStatusBarStartUpMenuBar$AllowShortcutMenusAllowFullMenus(AllowBuiltInToolbars&AllowToolbarChanges AllowSpecialKeysAppIcon,StartupShortcutMenuBar&UseAppIconForFrmRpt.Use Default Page Folder0HaveSetDefaultPageFolder   08.50            MR2ANSI Query ModeAccessVersion BuildProjVerHasCustomGroupsAppTitleStartUpForm&StartUpShowDBWindow(StartUpShowStatusBarStartUpMenuBar$AllowShortcutMenusAllowFullMenus(AllowBuiltInToolbars&AllowToolbarChanges AllowSpecialKeysAppIcon,StartupShortcutMenuBar&UseAppIconForFrmRpt.Use Default Page Folder0HaveSetDefaultPageFolder   08.50                 MR2ODBCTimeoutMaxRecordsRecordLocksRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLReplicable <      b Z U'ςO>;{%Xp@gamenGsM U\"[p@game-game subsetq9g0MCҜ'ςO>;{name!hdRI3 'ςO>;{gameid ^@xnGsM U\childidvnM.;FF'MnGsM U\parentid  ޿Cc]7uRMR2 GUIDNameMap b!H3r:-&  U ޿Cc]7uR_L=wp@Superset Queryq9g0MCҜ ޿Cc]7uRgame.nameq9g0MCҜ ޿Cc]7uRgame_1.nameMR2 GUIDNameMap (0zuHJyPr  U^OSCBv)T wp@Subset Queryq9g0MCҜ^OSCBv)game.nameq9g0MCҜ^OSCBv)game_1.nameMR2 GUIDNameMap B~&,N*~o^ V U*󝔆@jCH+)'bn@References Assigned to JennV㛃H/ӯon*󝔆@jCH+titlek&%^) Lѳeŷ*󝔆@jCH+authors㩻'O-s*󝔆@jCH+assignment details9@N#_*󝔆@jCH+comment LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete LVALMR2 GUIDNameMap&  L6D5͆  U|욳[J7j1QS|-x@Generatorsq9g0MCҜ|욳[J7j1Qname{|N@٠Ym|욳[J7j1Qdescription NߜpZv|욳[J7j1Qextensible-actionUE]=,J&ZbN|욳[J7j1Qgeneratei J N'|욳[J7j1Qis generatorѴa|F5AL|욳[J7j1Qentered 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"B-"0000Code Postal (international)B-1140_Belgium (French)~^\PP   0000Numro de Code Postal4212_Belgium (French)fFD<<   000000 000 00Numro de Registre National660909 353 14_Belgium (French)vtZZ$   000.000.000Numro de TVA (BTW)123.252.252_Belgium (French)~^\FF   000 0000009Numro de tlphone124 123456_Belgium (French)|\ZFF   000 0000000 00Numro de carte d'identit175 1234567 21_Belgium (French)xvZZ&  "B "0000Postcode (Belg)pZero-Sum Games )Welfare GamepWar of attrition6pUniform Local-Effect Game with clique-Uniform Local-Effect Game!!)Unbalanced Game#)Tree Structured Game)Travellers DilemmapStag and Hare-)Soccer Game)Small Pig)Simplified Poker)Simple Point Catcher Game!)Simple Inspection Game%)Shapley's GamepSecond price auctions formulated as strategic game:pSAT Games)Rock, Paper, ScissorspRoad GamepRing structured game()Random GamesPrisoner's DilemmapPotential Games+)Parallel Network GamespN-Player Prisoner s Dilemma&)N-Player Chicken*)Network Games)Morra pModern Manufacturing)Modeller's DilemmapMatching PenniespMajority VotingpLocation GamesLocal-Effect GamespInspection Game))Hotellings Game)Hero pHawk and Dove,)Grid Game)Greedy GamepGrab the Dollar7)FriendspFirst price auctions formulated as strategic games:")Exponential Game pDrilling for Oil)Dispersion Games)Discoordination Games pDiamond-Type Search Model! )Dangerous CoordinationpCournot DuopolyCoordination Game)Convergence )Contribution Games$)Congestion Games )Compound Games;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete{{M `B t 3  b A $  s T '  m I 1 g O 5  [<!ztowy99-878_PolandH<:..  !900\-00\-00Numer telefonu661-54-05PolandMR2ODBCTimeoutMaxRecordsOrderByOnOrientationSccStatusReplicableGUID4 <   MR2OrderByOnDescriptionColumnWidthColumnOrderColumnHiddenCaptionRequiredAllowZeroLengthDisplayControlIsShortcut; & Information Log{ObjType   $ Type of Object   mPropertySet a  2 *Property that was set   mO ID    Primary Key{ObjName   $ Name of Object   mlSetting    Setting    MR2FilterOnOrderByOnDefaultValueColumnWidthColumnOrderColumnHiddenFilterLookupDecimalPlacesRequiredDisplayControlAllowZeroLength  \ ID" GenUniqueID()    f StrId  0       m jPropertyName ]       m MR2ODBCTimeoutMaxRecordsOrderB)pZero-Sum Games )Welfare GamepWar of attrition6pUniform Local-Effect Game with clique-Uniform Local-Effect Game!!)Unbalanced Game#)Tree Structured Game)Travellers DilemmapStag and Hare-)Soccer Game)Small Pig)Simplified Poker)Simple Point Catcher Game!)Simple Inspection Game%)Shapley's GamepSecond price auctions formulated as strategic game:pSAT Games)Rock, Paper, ScissorspRoad GamepRing structured game()Random GamesPrisoner's DilemmapPotential Games+)Parallel Network GamespN-Player Prisoner s Dilemma&)N-Player Chicken*)Network Games)Morra pModern Manufacturing)Modeller's DilemmapMatching PenniespMajority VotingpLocation GamesLocal-Effect GamespInspection Game))Hotellings Game)Hero pHawk and Dove,)Grid Game)Greedy GamepGrab the Dollar7)FriendspFirst price auctions formulated as strategic games:")Exponential Game pDrilling for Oil)Dispersion Games)Discoordination Games pDiamond-Type Search Model! )Dangerous CoordinationpCournot DuopolyCoordination Game)Convergence )Contribution Games$)Congestion Games )Compound Games;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete LVALMR2 GUIDNameMap6  L6D5͆   U|욳[J7j1QS|-x@Generatorsq9g0MCҜ|욳[J7j1QName{|N@٠Ym|욳[J7j1QDescription NߜpZv|욳[J7j1Qextensible-actioni J N'|욳[J7j1Qis generatorУAљz@ܗ|욳[J7j1Qextensible-player...B.,v\U\o@7 0game-reference subform1|C@a3-]n@game-referenceeSUnFJ ⩛|C@a3-gameid!hdRI3 |욳[J7j1Qgameid\DE4ѽ3#՘@ 0game-game subset subformnGsM U\"[p@<game-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childidd J۩c1%+՘@ 0game-game subset subform1 LVALMR2 GUIDNameMap6  L6D5͆   U|욳[J7j1QS|-x@Generatorsq9g0MCҜ|욳[J7j1QName{|N@٠Ym|욳[J7j1QDescription NߜpZv|욳[J7j1Qextensible-actioni J N'|욳[J7j1Qis generatorУAљz@ܗ|욳[J7j1Qextensible-player...B.,v\U\o@7 0game-reference subform1|C@a3-]n@game-referenceeSUnFJ ⩛|C@a3-gameid!hdRI3 |욳[J7j1Qgameid\DE4ѽ3#՘@ 0game-game subset subformnGsM U\"[p@l game-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childidd J۩c1%+՘@ 0game-game subset subform1LVAL ^^{tmf_XQJC<5.'  xqjc\UNG@92+$Generalization of the anti-coordination game to arbitrary numbers of agents and actions. Agents prefer outcomes in which the agents are maximalGeneralization of the anti-coordination game to arbitrary numbers of agents and actions. Agents prefer outcomes in which the agents are maximally dispersed over the set of all actions.Games in which only one of the gains of a player as he shifGeneralization of the anti-coordination game to arbitrary numbers of agents and actions. Agents prefer outcomes in which the agents are maximally dispersed over the set of all actions.Games in which only one of the gains of a player as he shifts from his maximin to his minimax strategy while the co-player stays with the maximin is positive or zero.Games in which the gains of each player as he shifts from his maximin to his minimax strategy while the co-player stays with the maximin are both zero.Reference given to "Game Theory as a Tool for the Moral Philosopher" by Braithwaite (1955) Games in which the gains of each player as he shifts from his maximin to his minimax strategy while the co-player stays with the maximin are both positive. "Two Musicians" game is an example -- reference given in "Braithwaite's Arbitration Scheme" to pages 145-146 of Luce and Raiffa's "Games and Decisicions."Games in which the gains of each player as he shifts from his maximin to his minimax strategy while the co-player stays with the maximin are both negative.Games which have evolutionarily stable strategies. An evolutionarily stable strategy p is a strategy that meets the following 2 conditions: 1. p is an equilibrium strategy, i.e. it is a best response to itself 2. for every alternative best reply r to p, the following inequality holds: E(p, r) > E(r, r) where E is the payoff function Every 2X2 symmetric game has an evolutionarily stable strategy!! But not every 2 player symmetric game with arbitrary numbers of actions (counterexample: rock paper scissors) LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding completenI)pF j " p K ! g H ) _ 2  u V - )Weakly Dominant Strategies"4pWeak Equilibrium3pUnique Equilibrium5)Tractable Pure-Strategy Equilibria* )Timing Game:pThreat-Vulnerable Games)Symmetric Games (weak sense)$(pSymmetric Games (strong sense)& pSupermodular Games2pStrict Equilibrium0)Small Neighbourhood&pSeparable Games1pPure-strategy equilibrium!8pPure Coordination)Preemption Games%pPolymatrix Games/pPerfect Equilibria Exist .pPareto ordered / Strictly Better Equilibria Exist9$pNon-Braithwaite Games-pNo pure-strategy Nash when N > 3(,pNo Pure-Strategy Equilibria#9pNo dominant strategies#pMixed-Motive Games.)Markov Games3)k-Bounded Treewidth Games!/)k-Bounded Neighbourhood4)k-Bounded Hypertree-width!6)Intersection of bounded treewidth and small neighbourhoodA!pImproper Braithwaite Games"+pImperfect Equilibria pGraphical Games)Geometric Games;pForce-Vulnerable Games)Evolutionarily Stable Strategies(pDominant Strategies for All#)Dominance-Solvable Equilibrium&7pConstant-Sum Games)Complete OppositionpCompact Representation"pClassical Matrix GamepBraithwaite GamespAnti-Braithwaite Games')All payoffs are unique&)All NE's have index 12)'@ !@ !Graphical Games11  LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding completenI)pF j " p K ! g H ) _ 2  u V - )Weakly Dominant Strategies"4pWeak Equilibrium3pUnique Equilibrium5)Tractable Pure-Strategy Equilibria* )Timing Game:pThreat-Vulnerable Games)Symmetric Games (weak sense)$(pSymmetric Games (strong sense)& pSupermodular Games2pStrict Equilibrium0)Small Neighbourhood&pSeparable Games1pPure-strategy equilibrium!8pPure Coordination)Preemption Games%pPolymatrix Games/pPerfect Equilibria Exist .pPareto ordered / Strictly Better Equilibria Exist9$pNon-Braithwaite Games-pNo pure-strategy Nash when N > 3(,pNo Pure-Strategy Equilibria#9pNo dominant strategies#pMixed-Motive Games.)Markov Games3)k-Bounded Treewidth Games!/)k-Bounded Neighbourhood4)k-Bounded Hypertree-width!6)Intersection of bounded treewidth and small neighbourhoodA!pImproper Braithwaite Games"+pImperfect Equilibria pGraphical Games)Geometric Games;pForce-Vulnerable Games)Evolutionarily Stable Strategies(pDominant Strategies for All#)Dominance-Solvable Equilibrium&7pConstant-Sum Games)Complete OppositionpCompact Representation"pClassical Matrix GamepBraithwaite GamespAnti-Braithwaite Games')All payoffs are unique&)All NE's have index 12$.@.@Braithwaite Games33 nI)pF j " p K ! g H ) _ 2  u V - )Weakly Dominant Strategies"4pWeak Equilibrium3pUnique Equilibrium5)Tractable Pure-Strategy Equilibria* )Timing Game:pThreat-Vulnerable Games)Symmetric Games (weak sense)$(pSymmetric Games (strong sense)& pSupermodular Games2pStrict Equilibrium0)Small Neighbourhood&pSeparable Games1pPure-strategy equilibrium!8pPure Coordination)Preemption Games%pPolymatrix Games/pPerfect Equilibria Exist .pPareto ordered / Strictly Better Equilibria Exist9$pNon-Braithwaite Games-pNo pure-strategy Nash when N > 3(,pNo Pure-Strategy Equilibria#9pNo dominant strategies#pMixed-Motive Games.)Markov Games3)k-Bounded Treewidth Games!/)k-Bounded Neighbourhood4)k-Bounded Hypertree-width!6)Intersection of bounded treewidth and small neighbourhoodA!pImproper Braithwaite Games"+pImperfect Equilibria pGraphical Games)Geometric Games;pForce-Vulnerable Games)Evolutionarily Stable Strategies(pDominant Strategies for All#)Dominance-Solvable Equilibrium&7pConstant-Sum Games)Complete OppositionpCompact Representation"pClassical Matrix GamepBraithwaite GamespAnti-Braithwaite Games')All payoffs are unique&)All NE's have index 1%@ !~@$#Compact Representation88 NJJIIFF  !childidgame-game subsetch  !referenceidgame-referencereferenceidgame-reference subform1.referenceidbL00  !gameidgame-referencegameidg)@ !@ !Classical Matrix Game77  LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding completenI)pF j " p K ! g H ) _ 2  u V - xqjc\UNG@92+$ cccc cc)Weakly Dominant Strategies"4pWeak Equilibrium3pUnique Equilibrium5)Tractable Pure-Strategy Equilibria* )Timing Game:pThreat-Vulnerable Games)Symmetric Games (weak sense)$(pSymmetric Games (strong sense)& pSupermodular Games2pStrict Equilibrium0)Small Neighbourhood&pSeparable Games1pPure-strategy equilibrium!8pPure Coordination)Preemption Games%pPolymatrix Games/pPerfect Equilibria Exist .pPareto ordered / Strictly Better Equilibria Exist9$pNon-Braithwaite Games-pNo pure-strategy Nash when N > 3(,pNo Pure-Strategy Equilibria#9pNo dominant strategies#pMixed-Motive Games.)Markov Games3)k-Bounded Treewidth Games!/)k-Bounded Neighbourhood4)k-Bounded Hypertree-width!6)Intersection of bounded treewidth and small neighbourhoodA!pImproper Braithwaite Games"+pImperfect Equilibria pGraphical Games)Geometric Games;pForce-Vulnerable Games)Evolutionarily Stable Strategies(pDominant Strategies for All#)Dominance-Solvable Equilibrium&7pConstant-Sum Games)Complete OppositionpCompact Representation"pClassical Matrix GamepBraithwaite GamespAnti-Braithwaite Games')All payoffs are unique&)All NE's have index 1(.@.@Improper Braithwaite Games<< nI)pF j " p K ! g H ) _ 2  u V - SSSSS)Weakly Dominant Strategies"4pWeak Equilibrium3pUnique Equilibrium5)Tractable Pure-Strategy Equilibria* )Timing Game:pThreat-Vulnerable Games)Symmetric Games (weak sense)$(pSymmetric Games (strong sense)& pSupermodular Games2pStrict Equilibrium0)Small Neighbourhood&pSeparable Games1pPure-strategy equilibrium!8pPure Coordination)Preemption Games%pPolymatrix Games/pPerfect Equilibria Exist .pPareto ordered / Strictly Better Equilibria Exist9$pNon-Braithwaite Games-pNo pure-strategy Nash when N > 3(,pNo Pure-Strategy Equilibria#9pNo dominant strategies#pMixed-Motive Games.)Markov Games3)k-Bounded Treewidth Games!/)k-Bounded Neighbourhood4)k-Bounded Hypertree-width!6)Intersection of bounded treewidth and small neighbourhoodA!pImproper Braithwaite Games"+pImperfect Equilibria pGraphical Games)Geometric Games;pForce-Vulnerable Games)Evolutionarily Stable Strategies(pDominant Strategies for All#)Dominance-Solvable Equilibrium&7pConstant-Sum Games)Complete OppositionpCompact Representation"pClassical Matrix GamepBraithwaite GamespAnti-Braithwaite Games')All payoffs are unique&)All NE's have index 1* @@!Mixed-Motive Games44  LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete LVALMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q  U'ςO>;{͗՘@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedŗ`AjD&*,'ςO>;{coding complete LVALMR2 GUIDNameMap6  L6D5͆   U|욳[J7j1QS|-x@Generatorsq9g0MCҜ|욳[J7j1QName{|N@٠Ym|욳[J7j1QDescription NߜpZv|욳[J7j1Qextensible-actioni J N'|욳[J7j1Qis generatorУAљz@ܗ|욳[J7j1Qextensible-player...B.,v\U\o@7 0game-reference subform1|C@a3-]n@game-referenceeSUnFJ ⩛|C@a3-gameid!hdRI3 |욳[J7j1Qgameid\DE4ѽ3#՘@ 0game-game subset subformnGsM U\"[p@l game-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childidd J۩c1%+՘@ 0game-game subset subform1nI)pF j " p K ! g H ) _ 2  u V - ee)Weakly Dominant Strategies"4pWeak Equilibrium3pUnique Equilibrium5)Tractable Pure-Strategy Equilibria* )Timing Game:pThreat-Vulnerable Games)Symmetric Games (weak sense)$(pSymmetric Games (strong sense)& pSupermodular Games2pStrict Equilibrium0)Small Neighbourhood&pSeparable Games1pPure-strategy equilibrium!8pPure Coordination)Preemption Games%pPolymatrix Games/pPerfect Equilibria Exist .pPareto ordered / Strictly Better Equilibria Exist9$pNon-Braithwaite Games-pNo pure-strategy Nash when N > 3(,pNo Pure-Strategy Equilibria#9pNo dominant strategies#pMixed-Motive Games.)Markov Games3)k-Bounded Treewidth Games!/)k-Bounded Neighbourhood4)k-Bounded Hypertree-width!6)Intersection of bounded treewidth and small neighbourhoodA!pImproper Braithwaite Games"+pImperfect Equilibria pGraphical Games)Geometric Games;pForce-Vulnerable Games)Evolutionarily Stable Strategies(pDominant Strategies for All#)Dominance-Solvable Equilibrium&7pConstant-Sum Games)Complete 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'x'@  3(,pNo Pure-Strategy Equilibria#9pNo dominant strategies#pMixed-Motive Games.)Markov Games3)k-Bounded Treewidth Games!/)k-Bounded Neighbourhood4)k-Bounded Hypertree-width!6)Intersection of bounded treewidth and small neighbourhoodA!pImproper Braithwaite Games"+pImperfect Equilibria pGraphical Games)Geometric Games;pForce-Vulnerable Games)Evolutionarily Stable Strategies(pDominant Strategies for All#)Dominance-Solvable Equilibrium&7pConstant-Sum Games)Complete OppositionpCompact Representation"pClassical Matrix GamepBraithwaite GamespAnti-Braithwaite Games')All payoffs are unique&)All NE's hSupeSupermodular Games@Supermodular GamesHH44((4LVALme subset subformrm1m0hs0hs0p;wwo/aw0ͫ0iw0iwiw$p[iwiwPgame-game subset subform1m1m0hs0hs0p;wwo/aw0ͫ0iw0iwiw$p[iwiwPgame-reference subform31m1m0hs0hs0p;wwo/aw0ͫ0iw0iwiw$p[iwiwxPgenerator coding queue1m1m0hs0hs0p;wwo/aw0ͫ0iw0iwiw$p[iwiwdGAMUT Algorithmsqueue1m1m0hs0hs0p;wwo/aw0ͫ0iw0iwiw$p[iwiwdGAMUT 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Game)Greedy GamepGrab the Dollar7)FriendspFirst price auctions formulated as strategic games:")Exponential Game pDrilling for Oil)Dispersion Games)Discoordination Games pDiamond-Type Search Model! )Dangerous CoordinationpCournot DuopolyCoordination Game)Convergence )Contribution Games$)Congestion Games )Compound GamesHero,&LVAL* hh8x0`B t 3  b A $  s T '  m I 1 g O 5  [<!Games which are both 2x2 and symmetric All players have the same actions available to them. If two players exchange actions, their payoffs are also exchanged and everyone else's payoffs remain the same."Supermodular games are games in which each player's strategy set is partially ordered, the marginal returns to increasing one's strategy rise with increases in the competitors' strategies (so that the game exhibits 'strategic complementarity') and, if a player's strategies are multidimensional, the marginal returns to any one component of the player's strategy rise with increases in the other components." TODO: Determine f these are actually dominance-solvable. Not sure.Games which are both 2x2 and symmetric are interesting to list as their own set because they are a subset of games with evolutionarily stable strategiesPayoff for a player is determined by a formula a + bM - cE where E is the player's effort and M is the minimum effort of any player. Game is interesting when the values of a, b, and c are such that players will gain the most by all cooperating and exerting effort, but will be tempted to exert less effort if they think other players will also."Each person must claim a money amount, and the payment is the minimum of the claims, plus a (possibly small) payment incentive to be the low claimant. Both would be better off making identical high claims, but each has an incentive to 'undercut' the other to obtain the reward for having the lower claim." Introduced by Basu in 1994 Another reference given to Capra et al. 1999 All of chapter 12 is devoted to travelor's dilemma in Recipes for Interactive Learning, lots of empirical results and such --- Similar to centipede game in a matrix form. The only thing that survives dominance elimination is the outcome that nobody likes. 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l2lZlzlll(lPlplllllll l2lZlzll         game.namegamegame.descriptiongame.generate'game.coding priority'game.coding completelllll%uu@ll  lHI2lH ZlH zlH  lH gamel  llHlluu@#coding queue querylll (l l Pl(l  0l`l  hlll(lPl+game.[coding priority]0l+game.[coding complete]hl lH2lHZlH+zlH lHgame l@ l 2lH l ZlP l zlX l l` ll(lPl0lhl lll l8lPlhlllh llh llh llh llh llh llh llh llh llh llh llh llh llh llh llh llh llh llh llh llh llh llh llh llh llh llh llh llh llh llllllHl lHl $lHl $PlHl  PlHl lz xlPllxl0l hl`l lplllll 0l hl lll<HlPlXl`lhl0lhllllHlgame ll l#0ltobeincludedgamePrimaryKeypeoplegame gameidHllwv Hl8l9k09&llqllllllllllllllllllllllllllllll h lll`lgamePll Pll Pll PllHlll(ll8llHlllxll|l Hl&%game.[is generator] llhllXll llllltobeincludedgame l l̰ lll lDll ll llllll@PllPlllPlPllPllHlScP=) y f R ? ???????????????????????????????????????, ˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˢˏ    { h U A . ..................... ~jWWWWW o`zzi 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Z=m? z=m? =m? game=m  =m=mH=m=muu@#coding queue query=m=m=m (=m =m P=m(=m  0=m`=m  h=m=m=m(=mP=m+game.[coding priority]0=m+game.[coding complete]h=m =m?2=m?PZ=m? z=m? =m? game =m@ =m 2=mH =m Z=mP =m z=mX =m =m` =m=m(=mP=m0=mh=m =m=m=m =m8=mP=mh=m=m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=mh =m=m=m=m=m=mH=m =mH=m $=mH=m $P=mH=m  P=mH=m =mz x=mP=m=mC=m0=m h=m`=m =mp=m=m=m=m=m 0=m h=m =m=m=m<H=mP=mX=m`=mh=m0=mh=m=m=m=mH=mgame =m=m =m#0=mtobeincludedgamePrimaryKeypeoplegame gameidH=m=mv H=m8=m9k09&=m=m=qm=m=m=m=m=m=m=m=m=m=m=m=m=m=m=m=m=m=m=m=m=m=m=m=m=m=m=m=m=m h =m=m=m`=mgameP=m=m P=m=m P=m=m P=m=mH=m=m=m(=m=m8=m=mH=ml=mx=m=m|=m H=m&%game.[is generator] =m=mh=m=mX=m=m =m=m=m=m=mtobeincludedgame =m =m$t =m=m=m =mD=m=m =m=m =m=m=m=m=m=m@P=m=mP=m=m=mP=mP=m=mP=m=mH=m  ɕ m :  n;o< p= q> r? s@ tAuB#o  i>h33 tZڮj<4i3 ~r {p33 90j3 a%r33 ٟo  Nعo   zp3 Ǵ׺lgn  fn a r 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ggame.generate3 3 g game.description9 3 ggame.name+ 3s ggame s gj@+  g ) )Arms Racesl@9@Arms RacesDD8, 7R Ƿ******** * * **DOLGUID <      Ui^'`BYU,@tblStylesi^'`Bi^'`BObjectTypei^'`Bi^'`BStyleIDMR2ODBCTimeoutMaxRecordsOrderByOnRecordsetTypeOrientationSccStatusReplicableRecordLocks FilterOrderByNameMapDOLGUID(MR2ODBCTimeoutMaxRecordsRecordLocksRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLQ <       gL۪H4n  U'ςO>;{uu@gameL~Jޘ)9g'ςO>;{includedi J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{descriptionUE]=,J&ZbN'ςO>;{generateHyWBA?OV'ςO>;{coding priorityŗ`AjD&*,'ςO>;{coding completeMR2 GUIDNameMap m㛷ZByW  UgL۪H4n%uu@coding queue queryq9g0MCҜgL۪H4nname{|N@٠YmgL۪H4ndescriptionUE]=,J&ZbNgL۪H4ngenerateHyWBA?OVgL۪H4ncoding priorityŗ`AjD&*,gL۪H4ncoding completeMR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLReplicable  <       URAP)&\o@referenceSFK0s zRAP)&assigned tozEIJۮ RAP)&in 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@IN0wp@_L=wp@Superset Query9?v@J}@bVVJ>>>>>>< `HTvp@Tvp@Subset Query9@.}FFF:::::::8 @Gvp@T wp@Subset Query9W;v@:@^RRF::::::8 `F`vp@Zvp@~sq_rgame-game subset96@4MR2KeepLocal TXLLLLLLJ `EZo@EZo@Sets of Games9@HHH<<<<<<<: @g|Yo@mpu@Generators9qr@|@&ZNNB6666664 `#n@#n@Unassigned References9b@ XXXLLLLLLLJ @QÏn@gn@Unassigned References9-@@|@NpddXLLLLLLJ `Fn@tu@reference Query9@|@XLL@@@@@@@> @saϗn@saϗn@~sq_rAll References In List9x @P4MR2KeepLocal TdXXXXXXV `C^ϗn@C^ϗn@All References In List9v@VOZZZNNNNNNNL @:,?n@-?n@~sq_cgame-reference subform~sq_creferenceid9 @74MR2KeepLocal Txxxxxxv `-n@n@~sq_fgame-reference subform29J @4MR2KeepLocal TfZZZZZZX `In@In@peoplereference9@@@@@@@@@@> %Jn@%Jn@References Assigned to Kevin9p@BfffZZZZZZZX @u)gEquivalent to potential gamesCongestion GamesO==?  < Y v  & WC*****  ygg 2o Y1j<+n  $n  G.z L졐e>p _l+eun  kOlVࠋj<ҷǠi3 "Ǡj *keEho Xm  Me3J蟉j< eN>j<-z @@`@ @   @`@@@@@@ J@D"@ J@D"  ("p   ("p ) )$)cH@@@ Compound Games:*?  i 6  j 7  k 8  l 9  m :  n;o< p= q> r? s@ tAuB1vNj3 &n3333  1f3Ҵl:k3 ei3 ZڳeԳlƳfųn  Ӌj3 'Ngd )Wn @lUgsgPr1f3o &m  ^raLm fm)p3 p2zҰd333 ;h 雰eym  xi3 ]fn.z)h33 }Ѻz gg3z 家lgޮgn  }lӀgHeyFe33fN٭m  έj<ho3  5Cj<߉p.n Fsj Sn3333  #Yj3 S\8f3qk33 ૕j<2g;{Ntu@gameq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byi J N''ςO>;{is generatorУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{includedQ>)GV'ςO>;{coding priorityQ鵮 L$['ςO>;{coding complete  'ςO>;{description            {|N@٠Ym("extensible-action       Yes/No  j  NߜpZv  Nogenerate            UE]=,J&ZbNQ gameid       !hdRI3 name  M       m    q9g0MCҜentered by         5  m Ѵa|F5ALis generator       Yes/No  j i J N'("extensible-player       Yes/No  No  j УAљz@ܗ{included         0  m L~Jޘ)9g$coding complete       Yes/No  j ŗ`AjD&*, LVAL,NjǐƐ####$v$o$p$q$r$s$t$u 33334$4$4$4$4$4$5$5$ 5$5MR2.ValidationRuleValidationTextOrientation 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D55E%E6Ǧ@Dw UEUUUUUe&ǦpDw e%e%e%e&Ǧ`Dw XeEeEeEeE&ǦpDw uMR2.ValidationRuleValidationTextOrientation FilterOrderByOrderByOnNameMapDefaultViewGUIDColumnWidthColumnOrderColumnHiddenDescription FormatInputMaskCaptionDefaultValueRequiredAllowZeroLengthDisplayControlIMEModeIMESentenceMode$UnicodeCompressionDecimalPlacesA    U'ςO>;{!vu@gameq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ςO>;{entered byi J N''ςO>;{is generatorУAљz@ܗ'ςO>;{extensible-playerL~Jޘ)9g'ςO>;{included\-MBf'ςO>;{coding priorityŗ`AjD&*,'ςO>;{coding complete  'ςO>;{description            {|N@٠Ym("extensible-action       Yes/No  j  NߜpZv  Nogenerate            UE]=,J&ZbNQ gameid       !hdRI3 name  M       m    q9g0MCҜentered by         5  m Ѵa|F5ALis generator       Yes/No  j i J N'("extensible-player       Yes/No  No  j УAљz@ܗ{included         0  m L~Jޘ)9g$coding complete       Yes/No  j ŗ`AjD&*,$coding priority         0  m YTT|x-JoPcm 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U'ςO>;{͗՘@gameq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{descriptionUE]=,J&ZbN'ςO>;{generate NߜpZv'ςO>;{extensible-actionMR2 GUIDNameMap \DE4ѽ3  UnGsM U\"[p@h"game-game subsetvnM.;FF'MnGsM U\parentid ^@xnGsM U\childid'ςO>;{͗՘@h"gameq9g0MCҜ'ςO>;{name!hdRI3 'ςO>;{gameidi J N''ςO>;{is generator LVAL @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @xyz{|}~ 33334$4$4$4$4$4$5$5$ 5$5$ 5$ 5$7$7$7$7$7$F FFF F F FF GG;GG?G@GAGBGCG DG EGD ia  ?iii ik !iiiiiiii   game.namegamegame.gameidiiii ipzu@ii i8 i8 gamei  pii( ii 'Δu@M~sq_cgame-reference subform2~sq_cgameidi i`i ihiiii8 i8 game ii iiii i8i` i i8i@iHiPiXiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiixii i i( i Pi( i`iz  iHi i;i i i@ i  i i0 i i i i( igame 0iXi pi#itobeincludedgamePrimaryKeypeoplegame gameidiiv iik_0ki8i8qi8i8i8i8i8i8i8i8i8i8i8i8i8i8i8i8i8i8i8i8i8i8i8i8i8i8i8i8ii iixii igamei i Pi i Pi iiP iiHiiXii ii @ Pi8ii8i Pi8iihiiiHii   Hii( i {tmf_XQJC<5.'  xqjc\UNG@92+$ AAAAAAA AAeIdLvLvExtraLvModule LvPropName OwnerParentIdRmtInfoLongRmtInfoShortTypeniYYIdParentIdName        BBBBBBBBBBB B B B B BBBBBBBB __________________ _ _ _ _ _________&u%u$u#u"u!u uu| @@Minimum Effort GamesB,  LVALNDD - -------------------------------------ͨ / +L+++++++++++++ ; ;;;;;;Df0l0 ?Xl0lX llAd <bllllll:lblXllllll0lXlplplplplplplplplbllllll:lbl              game.namegamegame.description+game.extensible-actiongame.generategame.gameidgame.entered by!game.is generatorgame.includedll Hllxlpu@ll bl(! l(! l(! l(! l(! l(! :l(! bl(! gamel  Hlllxl 'Δu@Sets of Gamesl Xll ll ll ll ll ll l8l Xl@lXll/game.[extensible-action]lll!game.[entered by]l%game.[is generator]lXl bl(!yl(!l(!%l(!.[l(!erl(!:l(!bl(!game bl l l l l( l l0 l l8 l l@ l :lH l blP lXlllllllXl llxl xl8lXlxlllX llX llX llX llX llX llX llX llX llX llX llX llX llX llX llX llX llX llX llX llX llX llX llX llX llX llX llX llX llX ll8l@llll ll $Pll ll $Pll`Pll  Pll  Pll  lz lll$l l Xllll lll(l8l8lplHllXl  l Xll ll8lpllH HlPlXl`lhlplxll lXllll8lplllgame ll 0l#HltobeincludedgamePrimaryKeypeoplegame gameid`llv `lPl0Adllqllllllllllllllllllllllllllllll X ll`llgamell Pll Pll`lhlllll<lHllLl l&%game.[is generator] ll8lPl(llll `ll @ ll Plllllll ll LVALDd0s0L ?Xs0sX ssAd <bssssss:sbsXssssss0sXspspspspspspspspsbssssss:sbs              game.namegamegame.description+game.extensible-actiongame.generategame.gameidgame.entered by!game.is generatorgame.includedss Hssxspu@ss bs( s( s( s( s( s( :s( bs( games  Hsssxs 'Δu@Sets of Gamess Xss ss ss ss ss ss s8s Xs@sXss/game.[extensible-action]sss!game.[entered by]s%game.[is generator]sXs bs( isys( ats( s( s( ls( l:s( bs( game bs s s s s( s s0 s s8 s s@ s :sH s bsP sXsssssssXs ssxs xs8sXsxsssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ssX ss8s@ssss ss $Pss ss $Pss`Pss  Pss  Pss  sz sss s s Xssss sss(s8s8spsHssXs  s Xss ss8spssH HsPsXs`shspsxss sXssss8spsssgame ss 0s#HstobeincludedgamePrimaryKeypeoplegame gameid`ssv `sPs0Adssqssssssssssssssssssssssssssssss X ss`ssgamess Pss Pss`shsssss<sHssLs s&%game.[is generator] ss8sPs(ssss `ss @ ss Psssssss ssLVAL Models situation of two rivalPayoff for each player is a sum of pNever has a PSNE Called "cycle games" in "A Taxonomy of 2x2 games" because "if the players pursue short-term gains, the plays will move around the cycle of outcomes."Payoff for each player is a sum of payoffs in two-player games against a subset of the other players Can be solved very efficiently by Lemke-HowsonModels situation of two rival firms choosing how to price their competing goods at the same time. Firm i's utility is given by (pi)(D(pi)/m) - Ci(D(pi)/m) if firm i is one of the m firms with the lowest price 0 otherwise where Ci(n) is the cost function for producing n goods D(n) is the demand function, i.e. the number of goods the public will want at price n m is the number of firms offering the product at the lowest price pi is the price chosen by firm iA simplification of the cournot duopoly game which has unit costs for producing goods, among other things. Q1 and Q2 are the quantities produced by each firm respectively. The actions of the game consist of setting these. a and b are variables having to do with market demand. c is the cost for producing a unit of the good The utility of firm i is given by: ui (Q1, Q2) = (a - b (Q1 + Q2))Qi - cQi for 0 <= Q1 + Q2 <= a/b -cQi for a/b < Q1 + Q2Let L be a rectangular lattic of points: L = { (i, j) : i = 1, 2, ..., n; j = 1, 2, ..., m} Let F be the collection of all functions f from {1, 2, ..., n} into {1, 2, ..., m} SAG is a geometric game in which the set B for the blue player is equal to F, and the set R for the red player consists of all subsets of L with no more than k members. The payoff to blue if blue plays f in B and red plays r in R is <f, r> which is defined as 1 if (i, f(i)) is in R for no i and 0 if (i, f(i)) is in R for some i. Also listed are: Ambush Game, Lattice Ambush Game, Multiple Ambush Game, Penetration Game some example stories and scenarios are given too LVALN>> ͫ0 k k ' '''''''''''''''''''''''''''''''˶ Q QQQQQQQQQQډ r j . q /  m ? d 6 Lf&}HvPg2&&&& & &&ppp p p p t OBOdgame.[is generator]4 /tOBOgame tBO game.gameid* gtBO game.name( gtOBO tBO Gs OBO game.name( 's OBOdgame.[is generator]4 /sOBOgame met people.id( gt people.name* gt t Gs OBO game.name( 's OBOdgame.[is generator]4 /sOBOgame sBO game.gameid* gsBO game.name( gsOBO sBO GrOripeople rri people.id( grri people.name* grOri rri GqOritobeincluded))) qritobeincluded.iDi88T ?X 8  4   d  people.name peoplepeople.idd F\u@ Re`1 ce `1 peoplenxX k2Zo@O~sq_cAssigned References~sq_cassigned to  h p  `1 OM`1 e;people      8@HPX                              xH  X  PX `z   c1   p   d  0    X  people8 P PrimaryKeyid`    v xP`  q                             0 peoplePrimaryKeyP x xP  X  TNAA ̄ B BBB˵ ʵʵʵ@ @@@@@@@@@@@@@@@@ p ppppppppppppppɻ@^ƔƔƔƔƔƔ5555555PmWou@(ou@~sq_cGenerators~sq_cText189@34MR2KeepLocal TbVVVVVVT `Vou@ou@~sq_cGenerators~sq_cgame-reference subform19 @24MR2KeepLocal Txxxxxxv `UP2ou@P2ou@~sq_cGenerators~sq_cgame-game subset subform9 @14MR2KeepLocal Tzzzzzzx `Toou@qou@~sq_cGenerators~sq_cgame-game subset subform19 @04MR2KeepLocal T||||||z `SxHXu@xHXu@tobeincludedgame9BBBBBBBBBB@ 2Wu@0IXu@tobeincluded9@FFF:::::::8 @JG=w @@`@ @  @ @`@@@@@MR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOL  <      |욳[J7j1Q8 0 U'ςO>;{0IXu@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{der(((reference.authors="Leyton-Brown, T((reference.authors="Leyton-Brown, Tennenholtz"))reference.[assigned to] = Lookup_Combo30.idSELECT pe#,@%Simple Ambush Game4 4LVAL > t^Not sure exactly what qualifies as partial dispersion since the definition is broad. Could generate a common payoff dispersion game and perturb some of the payoffs.??? Rationalizability paper doesn't give many details, and Modern Manufacturing paper seems to illustrate a very complicated game.May want to generate separately common preference dispersion games, selfish dispersion games, and partial dispersion games since the payoff structure is very different in all three. Roughly speaking, fill in all payoffs ordered such that a more dispersed outcome with always have a higher payoff for all players than a less dispersed outcome. How dispersed an outcome is can be measured in different ways, for example by calculating entropy or calculating standard deviation.Randomly generate values for P, R, S, and T, and also N such that N > 1. Generate payoff functions for each player as P(C) = Rx + S(N-x) P(D) = Tx + P(N-x) where C and D are the player's two action choicesFor a two-player version, generate a table: A, B C, C C, C B, A or C, C B, A A, B C, C such that either (C < A < B) or (C < B < A) Can use the formula in Compound Games to generate version with more players, although not sure how meaningful this would beParameterize on players and actions. Can generate a constant c in order to create cost function, and generate a constant a in order to create demand function, both as shown in the description. Then set payoff for each player to (pi)(D(pi)/m) - Ci(D(pi)/m) if firm i is one of the m firms with the lowest price 0 otherwiseParameterize a, b, and c, and on the range of choices available to the players for how many goods they can produce. Calculate utility functions as shown in the description. Generally I don't think more than 2 players are considered in a Cournot Duopoly game, but it seems like there is no reason we couldn't extend it to more by changing (Q1 + Q2) to (Q1 + Q2 + ... + QN) in the utility function. N]]erators~sq_cCombo319@T4MR2KeepLocal TdXXXXXXV `Wou@(ou@~sq_cGenerators~sq_cText189@34MR2KeepLocal TbVVVVVVT `Vou@ou@~sq_cGenerators~sq_cgame-reference subform19 @24MR2KeepLocal Txxxxxxv `UP2ou@P2ou@~sq_cGenerators~sq_cgame-game subset subform9 @14MR2KeepLocal Tzzzzzzx `Toou@qou@~sq_cGenerators~sq_cgame-game subset subform19 @04MR2KeepLocal T||||||z `SxHXu@xHXu@tobeincludedgame9BBBBBBBBBB@ 2Wu@0IXu@tobeincluded9@FFF:::::::8 @JG=wp@G=wp@SuD  ?    V !          d tobeincluded.idtobeincluded'tobeincluded.include(       pu@   H) Htobeincluded@      0IXu@;~sq_cSets of Games~sq_cCombo26       %[tobeincluded].[id] /[tobeincluded].[include]  Hre Hetobeincluded           (   8 @ H P X                                                             x  P  P  `    z           d 0     tobeincluded  PrimaryKeyid  v 0   reference.titl  !referenceidalgori#@%$@(Linear Cournot DuopolyD, +Nbb     @&\o@Tables~sq_fgame-reference subform3j2& -n@n@Tables~sq_fgame-reference subform2j2& ĝn@Fn@Tables~sq_fgame-reference subform1j2& ɘmn@5mn@Tables~sq_fgame-reference subformh2& [o@[o@Tables~sq_fgame-game subset subform1n2& eZo@:JZo@Tables~sq_fgame-game subset subforml2& DR+n@ S+n@Tables~sq_falgorithm-reference Subform1t2& Nm@Nm@Tables~sq_falgorithm-reference Subformr2& /~-zn@-zn@Tables~sq_falgorithmN2& !o@o@Tables~s @@`@ @  @ @`@@@@MR2RecordLocksODBCTimeoutMaxRecordsRecordsetType FilterOrderByOrderByOnOrientationNameMapDefaultViewGUIDDOLReplicable  <     &  U'ςO>;{0IXu@gamei J N''ςO>;{is generatorq9g0MCҜ'ςO>;{name{|N@٠Ym'ςO>;{description NߜpZv'ςO>;{extensible-actionUE]=,J&ZbN'ςO>;{generate!hdRI3 'ςO>;{gameidѴa|F5AL'ς iAn Introduction to Game Theory (draft of Chapter 3)Martin Osbornej@O?  LVAL Ь ʬv:`B "GloTODO: See reference to Hamburger 1969 These games can be presented to experimental subjects to bring out psychological aspects, but unsure of what they areAll players guess a number between 0 and 100. The one who guesses closest to 2/3 of the total average gets a high payoff, all others get 0. Only equibrium is for everyone to guess 0.Dispersion games in which agents may be selfish, i.e. they may prefer individually to use a resource with the fewest possible other users, regardless of the welfare of the rest of the group. These are non-common-preference dispersion games.Is this idea extensible? What would it mean for more actions or more players? Two player version has single equilibrium in mixed strategies.Games which have neutral stable strategies. This is a weakening of evolutionarily stable strategies that accounts for games like rock paper scissors that don't meet the criteria for ESS but seem to be stable. An evolutionarily stable strategy p is a strategy that meets the following 2 conditions: 1. p is an equilibrium strategy, i.e. it is a best response to itself 2. for every alternative best reply r to p, the following inequality holds: E(p, r) >= E(r, r) where E is the payoff function <- the >= instead of > here is how this differs from ESS Other weaker variations of ESS exist as wellJust as in regular Bertrand Oligopoly, firms each choose a price pi from some range Firm i's utility is given by (pi)(D(pi)/m) - Ci(D(pi)/m) if firm i is one of the m firms with the lowest price 0 otherwise where Ci(n) is the cost function for producing n goods D(n) is the demand function, i.e. the number of goods the public will want at price n m is the number of firms offering the product at the lowest price pi is the price chosen by firm I In the unit cost and linear demand function version, functions are simplified: Can use a unit cost function Ci(n) = (c)(n) for some c Can use D(n) = a - n for n <= a 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