Games of Incomplete Information Played by Statisticians

45 Pages Posted: 13 Mar 2017 Last revised: 5 Mar 2018

Annie Liang

University of Pennsylvania

Date Written: February 28, 2018


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 various solutions. This number of observations needed depends on the degree of strictness of the solution and speed of common learning.

Keywords: heterogeneous priors, beliefs, robustness, learning

Suggested Citation

Liang, Annie, Games of Incomplete Information Played by Statisticians (February 28, 2018). Available at SSRN: or

Annie Liang (Contact Author)

University of Pennsylvania ( email )

Philadelphia, PA 19104
United States

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