Interim correlated rationalizability in large games

TL;DR

This paper develops a theoretical framework for modeling strategic uncertainty in large Bayesian games using interim correlated rationalizability, especially in supermodular payoff settings, and illustrates it with large electronic mail and global games.

Contribution

It introduces a general theoretical foundation for interim correlated rationalizability in large games without assuming order on types, linking it to extremal equilibria.

Findings

Extremal interim correlated rationalizable solutions correspond to extremal Bayes-Nash equilibria.

Framework applies to large electronic mail and global games.

No order structure on types is required.

Abstract

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.