We furnish conditions on the primitives of a Bayesian game that guarantee the existence of a Bayes-Nash equilibrium. By allowing for payoff discontinuities in actions, we cover various applications that cannot be handled by extant results.

Polyequilibrium is a generalization of Nash equilibrium that is applicable to any strategic game, whether finite or otherwise, and to dynamic games, with perfect or imperfect information. It differs from equilibrium in specifying strategies that players do not choose and by requiring an...