Berk-Nash Equilibrium: A Framework for Agents

We develop an equilibrium framework that relaxes the standard assumption that people have a correctly-specified view of their environment. Each player is characterized by a (possibly misspecified) subjective model, which describes the set of possible beliefs (over distributions over others’ actions and payoff relevant states). We introduce the notion of a Berk-Nash equilibrium: Each player follows a strategy that is optimal given her belief, and her belief is restricted to be the best fit among the set of beliefs she considers possible. The notion of best fit is formalized in terms of minimizing the relative entropy and depends on the equilibrium strategy profile. Standard solution concepts such as Nash equilibrium and self-confirming equilibrium constitute special cases where players learn with correctly-specified models. The framework provides a systematic approach to modeling players with misspecified views and also unifies a specific bounded rationality literature where mistakes are driven by misspecifications. Importantly, we provide a learning foundation for Berk-Nash equilibrium by extending and combining results from the statistics literature on misspecified learning and the economics literature on learning in games. ∗We thank Vladimir Asriyan, Pierpaolo Battigalli, Larry Blume, Aaron Bodoh-Creed, Sylvain Chassang, Emilio Espino, Erik Eyster, Drew Fudenberg, Yuriy Gorodnichenko, Philippe Jehiel, Stephan Lauermann, Natalia Lazzati, Kristóf Madarász, Matthew Rabin, Ariel Rubinstein, Joel Sobel, Jörg Stoye, and several seminar participants for helpful comments. Esponda: Olin Business School, Washington University in St. Louis, 1 Brookings Drive, Campus Box 1133, St. Louis, MO 63130, [email protected]; Pouzo: Department of Economics, UC Berkeley, 530-1 Evans Hall #3880, Berkeley, CA 94720, [email protected].