  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.
