Interim correlated rationalizability in large games

We provide general theoretical foundations for modeling strategic uncertainty in large distributional Bayesian games with general type spaces, using a version of interim correlated rationalizability. We then focus on the case in which payoff functions are supermodular in actions, as is common in the literature on global games. This structure allows us to identify extremal interim correlated rationalizable solutions with extremal interim Bayes-Nash equilibria. Notably, no order structure on types is assumed. We illustrate our framework and results using the large versions of the electronic mail game and a global game.