Equilibria in infinite games of incomplete information

The notion of communication equilibrium extends Aumann's (J Math Econ 1:67-96, 1974, ) correlated equilibrium concept for complete information games to the case of incomplete information. This paper shows that this solution concept has the following property: for the class of incomplete information games with compact metric type and action spaces, and with payoff functions jointly measurable and continuous in actions, limits of Bayes-Nash equilibria of finite approximations to an infinite game are communication equilibria (and, in general, not Bayes-Nash equilibria) of the limit game. Stinchcombe's (J Econ Theory 146:638-655, 2011b, ) extension of Aumann's (J Math Econ 1:67-96, 1974, ) solution concept to the case of incomplete information fails to satisfy this condition.