We obtain conditions on the primitives of a Bayesian game with infinitely many types and/or strategies that ensure the existence of a perfect Bayes-Nash equilibrium. The main existence results are illustrated in the context of all-pay auctions.

The notion of communication equilibrium extends Aumann's [3] correlated equilibrium concept for complete information games to the case of incomplete information. This paper shows that this solution concept has the following property: for the class of incomplete information games with compact...

We show that supermodular games satisfying sequential better-reply security possess a pure strategy perfect equilibrium and a strategically stable set of pure strategies. We illustrate that, in continuous supermodular games, perfect equilibria may contain weakly dominated actions. Moreover, in...