% This program finds efficient/inefficient correlated equilibria that % maximize/minimize weighted sum of the payoffs in a two player normal form game % max/min w*U1(P)+(1-w)*U2(P) % s.t. P is correlated equilibrium % where U1 and U2 are given n-by-m matrices of payoffs of two players. % % Algorithm builds the linear inequalities that represent the rationality % constraints for two players. The constraint matrix A is constructed so that % if P is the probability distribution over joint actions, and if X=P(:), % the correlated equilibrium constraints are A * X <= 0. % % The program also plots the convex hull of found correlated equilibria % together with the convex hull of given Nash equilibria which can be % solved for by Gambit. http://gambit.sourceforge.net % % Author: % Iskander Karibzhanov % PhD student, Department of Economics % University of Minnesota % Example 1: Prisoner's dilemma u1=[6 1 5 0]; % payoff of player 1 u2=[0 1 5 6]; % payoff of player 2 ne=[1 0 0 1]; % Nash equilibria plotce(u1,u2,ne,'PRISONER''S DILEMMA') % Example 2: Battle of sexes u1=[3 0 0 1]; % payoff of player 1 u2=[1 0 0 3]; % payoff of player 2 ne=[[3 1 1 3]/4 0 1 0 1 1 0 1 0]; % Nash equilibria plotce(u1,u2,ne,'GAME OF BATTLE OF SEXES') % Example 3: Game of chicken (Aumann, 1974) u1=[5 0 4 1]; % payoff of player 1 u2=[1 0 4 5]; % payoff of player 2 ne=[[1 1 1 1]/2 0 1 0 1 1 0 1 0]; % Nash equilibria plotce(u1,u2,ne,'GAME OF CHICKEN (AUMANN, 1974)')