Correlated equilibrium and concave games

Abstract

This paper shows that if a game satisfies the sufficient condition for the existence and uniqueness of a pure-strategy Nash equilibrium provided by Rosen (Econometrica 33:520, 1965), then the game has a unique correlated equilibrium, which places probability one on the unique pure-strategy Nash equilibrium. In addition, it shows that a weaker condition suffices for the uniqueness of a correlated equilibrium. The condition generalizes the sufficient condition for the uniqueness of a correlated equilibrium provided by Neyman (Int J Game Theory 26:223, 1997) for a potential game with a strictly concave potential function.