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. The set of these equilibria is convex and lies between the symmetric Nash equilibria and the symmetric correlated equilibria. The notion of exchangeable equilibria admits several natural game-theoretic interpretations which emphasize their high degree of symmetry and suggest why they may be focal.