On the existence of equilibria to Bayesian games with non-finite type and action spaces

Equilibria are shown to exist in non-finite Bayesian games if the type and action spaces are compact and convex subsets of finite dimensional Euclidean space, utility functions are continuous, expected utility functions are strictly quasiconcave in the agent’s action, the set of rationalizable mappings have a uniformly bounded slope and posterior beliefs are suitably continuous.