Abstract:

The common prior assumption is a convenient restriction on beliefs in games of incomplete information, but conflicts with evidence that agents 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. I model players as statisticians who infer an unknown parameter from data. Players know that they may use different inference rules (and, therefore, may disagree about the distribution of payoffs), but have common certainty in the predictions of a class of inference rules. Using this framework, I study the robustness of solutions to a relaxation of the common prior assumption. The main results characterize which rationalizable actions and which Nash equilibria persist given finite quantities of data, and provide a lower bound on the quantity of data needed to learn these solutions. I suggest a new criterion for equilibrium selection based on statistical complexity--solutions that are ``hard to learn" are selected away.