Games of Incomplete Information Played By Statisticians

Last updated: August 10, 2016


Abstract. The common prior assumption is a convenient restriction on beliefs in games of incomplete information, but conflicts with evidence that players publicly disagree in many economic environments. This paper proposes a foundation for heterogeneous beliefs in games, in which disagreement arises not from different information, but from different interpretations of common information. A key assumption imposes that while players may interpret data in different ways, they have common certainty in the predictions of a class of interpretations. 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 quantity, which I refer to as the robustness of the solution, is shown to depend crucially on the degree of strictness of the solution and the "complexity" of inference from data.