On the Existence of Nash Equilibrium in Bayesian Games *

Abstract We furnish conditions on the primitives of a Bayesian game that guarantee the existence of a BayesNash equilibrium. We consider spaces of distributional and behavioral strategies, and highlight the relationship between their respective topologies, which implies that the two spaces are mutually interchangeable throughout the analysis. By allowing for payoff discontinuities in actions, we cover various applications that cannot be handled by extant results