Games of Incomplete Information Played by Statisticians

This paper proposes a foundation for heterogeneous beliefs in games, in which disagreement arises not because players observe different information, but because they learn from common information in different ways. Players may be misspecified, and may moreover be misspecified about how others learn. The key assumption is that players nevertheless have some common understanding of how to interpret the data; formally, players have common certainty in the predictions of a class of learning rules. The common prior assumption is nested as the special case in which this class is a singleton. The main results characterize which rationalizable actions and Nash equilibria can be predicted when agents observe a finite quantity of data, and how much data is needed to predict different solutions. This number of observations depends on the degree of strictness of the solution and the "complexity" of inference from data.