Large but finite games with asymmetric information

Carmona considered an increasing sequence of finite games in each of which players are characterized by payoff functions that are restricted to vary within a uniformly equicontinuous set and choose their strategies from a common compact metric strategy set. Then Carmona proved that each finite game in an upper tail of such a sequence admits an approximate Nash equilibrium in pure strategies. Noguchi (2009) and Yannelis (2009) recently proved that a Nash equilibrium in pure strategies exists in a continuum game with asymmetric information in which players are endowed with private information, a prior probability and choose strategies that are compatible with their private information and maximize their interim expected payoffs. The aim of this paper is to extend Carmona's result to the broader context of Bayesian equilibria and demonstrate that the existence result obtained for continuum games with asymmetric information approximately holds for large but finite games belonging to an upper tail of a sequence of finite games with asymmetric information.Nash equilibrium Approximate equilibria Large games Bayesian games Private information