On Purification of Equilibrium in Bayesian Games and Ex-Post Nash Equilibrium

Abstract

Kalai (2002) demonstrates that in semi anonymous Bayesian games with sufficiently many players any Bayesian equilibrium is approximately ex-post Nash. In this paper we demonstrate that the existence of an approximate expost Nash property implies a purification result of the standard sort for the original Bayesian game. We also provide an example showing that the bound we obtain on the distance of a purified approximate equilibrium from an exact equilibrium is tight.