Exchangeable Equilibria, Part I: Symmetric Bimatrix Games

We introduce the notion of exchangeable equilibria of a symmetric bimatrix game, defined as those correlated equilibria in which players' strategy choices are conditionally independently and identically distributed given some hidden variable. We give several game-theoretic interpretations and a version of the "revelation principle". Geometrically, the set of exchangeable equilibria is convex and lies between the symmetric Nash equilibria and the symmetric correlated equilibria. Exchangeable equilibria can achieve higher expected utility than symmetric Nash equilibria.