Interim correlated rationalizability in large games

In this paper we provide general theoretical foundations for modeling strategic uncertainty in large distributional Bayesian games with general type spaces (with aggregate uncertainty) in terms of a version of interim correlated rationalizability. We then focus on the case that payoff functions are supermodular in actions as in much literature on global games. This allows us to identify extremal interim correlated rationalizable solutions with extremal interim Bayes-Nash equilibria. No order structure on types is used. We prove the existence of a universal type space. We provide an example of a large version of the email game and an application to large global games without common prior.