Milgrom's 1985 paper with Robert J. Weber on distributional strategies showed the general existence of equilibria for a Bayesian game with finitely many players, if the players' sets of types and actions are compact metric spaces, the players' payoffs are continuous functions of the types and actions, and the joint distribution of the players' types is absolutely continuous with respect to the product of their marginal distributions. These basic assumptions are always satisfied if the sets of types and actions are finite.