On purification of equilibrium in Bayesian games and ex-post Nash equilibrium

Abstract

We demonstrate that if any realization for a Bayesian game is, with high profitability, an approximate Nash equilibrium of the induced game of complete information, then there is a purification of that strategy that is an approximate equilibrium of the original Bayesian game. We also provide two examples demonstrating, amongst other things, that the bound we obtain on the distance of the purification from satisfying the requirements for an exact equilibrium is tight