Characterization of equilibrium existence and purification in general Bayesian games
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.
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