Pure-strategy equilibria in Bayesian games

Abstract

A general condition called “coarser inter-player information” is introduced and shown to be necessary and sufficient for the validity of several fundamental properties on pure-strategy equilibria in Bayesian games, such as existence, purification from behavioral strategies, and convergence for a sequence of games. Our sufficiency results cover various earlier results on pure-strategy equilibria in Bayesian games as special cases. New applications are presented as illustrative examples, including auctions with externalities and risk-neutral bidders, and Bertrand pricing games with asymmetric information.