Generate a Local Effect Game with a given graphical
structure and a given function structure such that
the function stored on an edge a to b is the same as
the function stored on an edge b to a.
Class implements a specific kind of dispersion game:
both action symmetric and agent symmetric as defined in
the dispersion games literature, also strong,
and common payoff.
Generate the graph and for each node and edge of the graph,
a function, making sure that functions are the same on every
edge from a to b as they are on the edge from b to a.
Generates one payoff for every outcome, making sure that
all of the equilibrium outcomes (those on the diagonal
of the matrix) are higher than all of the non-equilibrium
outcomes and all equal.
Generate one payoff for every outcome, making sure that
all of the equilibrium outcomes (those on the diagonal
of the matrix) are higher than all of the non-equilibrium
outcomes.
Generate the symmetric 2x2 subgame and create a polymatrix
game with this 2x2 matrix at all edges except the edges
from nodes to themselves which will have stub 0 matrices.
Generates the graph and for each node and edge of the graph,
a function, making sure that functions are the same on every
edge from b to a as they are on the edge from c to a.
Sets up the compound game as a graphical game (polymatrix,
really) with each submatrix being in the form
R, R S, T
T, S P, P
for whatever values of R, S, T, and P are passed in.
It is more efficient to calculate all payoffs for all players
in a given outcome at once since the number of players who
have chosen each facility will only have to be calculated once.
Returns the payoff for the given player at the given
outcome, which must first be translated into subsets of
the elements which are chosen by each player.
Figures out payoff for a certain outcome by adding up
a) the payoff from the matrix that is stored at the
player's node if one exists
b) payoffs from all of the matrices which are connected
by edges to the node of a certain player, if any of
those exist
Sets the matrix for the player's node if using the version
of the graphical game representation in which the payoffs
are stored in matrices at the nodes (as opposed to only
on edges).
Sets the parameters for the payoff functions for the case
when the player has the lowest time, the case when the player
is tied, and the case when the player does not have the lowest
time.
Generate a Local Effect Game with a given graphical
structure and a given function structure such that
every edge from b to a has the same local effect as
an edge from c to a.