Existence of Bayesian Equilibria in Incomplete Information Games without Common Priors

We consider incomplete information finite-player games where players may hold mutually inconsistent beliefs without a common prior. We introduce absolute continuity of beliefs, extending the classical notion of absolutely continuous information in Milgrom and Weber (1985), and prove that a Bayesian equilibrium exists under broad conditions. Applying these results to games with rich type spaces that accommodate infinite belief hierarchies, we show that when the analyst's game has a type space satisfying absolute continuity of beliefs, the actual game played according to the belief hierarchies induced by the type space has a Bayesian equilibrium for a wide class of games. We provide examples that illustrate practical applications of our findings.