Large incomplete-information games with independent types

We consider Bayes-Nash equilibria of large semi-anonymous games (i.e., each player's payoff is determined by his type, his action, and the distribution of the realized types and choices of the others). In a model with finite type and action spaces, we provide a characterization of limits of sequences of Bayes-Nash equilibria as the number of players goes to infinity. Based on this, we show that strict pure-strategy Bayes-Nash equilibria exist in all sufficiently large finite-player games for generic distributions of players' payoff functions and type distributions.