Characterization of equilibrium existence and purification in general Bayesian games

TL;DR

This paper establishes conditions for the existence of pure-strategy equilibria and purification in complex Bayesian games with general action spaces, interdependent payoffs, and discontinuities, advancing game theory understanding.

Contribution

It introduces the decomposable coarser payoff-relevant information condition, proving its necessity and sufficiency for equilibrium existence and purification in Bayesian games.

Findings

Pure-strategy equilibria exist under the new condition.

Purification from behavioral strategies is achievable.

Results apply to oligopoly and auction models.

Abstract

This paper studies Bayesian games with general action spaces, correlated types and interdependent payoffs. We introduce the condition of ``decomposable coarser payoff-relevant information'', and show that this condition is both sufficient and necessary for the existence of pure-strategy equilibria and purification from behavioral strategies. As a consequence of our purification method, a new existence result on pure-strategy equilibria is also obtained for discontinuous Bayesian games. Illustrative applications of our results to oligopolistic competitions and all-pay auctions are provided.