Stability in large Bayesian games with heterogeneous players

Bayesian Nash equilibria that fail to be hindsight-(or, alternatively, ex-post) stable do not provide reliable predictions of outcomes of games in many applications. We characterize a family of large Bayesian games (with many players) in which all equilibria are asymptotically hindsight-stable, and discuss the consequences of this robustness property. In contrast to earlier literature, we establish hindsight stability in a class of games in which players are not anonymous and type spaces and action spaces can be infinite.