The Set of Correlated Equilibria 2 x 2 Games

We develop a geometric procedure to get all correlated equilibria in a 2 x 2 game. With this procedure we can actually "see" all the correlated strategy profiles of a given game and compare it to the convex hull of the Nash equilibrium profiles. Games without dominant strategies fall into two different equivalence classes: (i) competitive games, that have a unique correlated equilibrium strategy, and (ii) coordination and anticoordination games, whose set of correlated equilibria is a polytope with five vertices for which we provide general closed-form expressions. In this latter case, there are either three or four vertices for the payoffs. In contrast, the convex hull of the Nash equilibrium strategies and payoffs always have three vertices.