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 feasible beliefs over payoff-relevant consequences as a function of actions. 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 Kullback-Leibler divergence, which is endogenous and depends on the equilibrium strategy profile. Standard solution concepts such as Nash equilibrium and self-confirming equilibrium constitute special cases where players have correctly-specified models. 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 experimentally document persistence of suboptimal behavior despite ample opportunities to learn from feedback in a canonical updating problem where people suffer from base-rate neglect. Our results provide insights on the mechanisms hindering learning from feedback. Importantly, our results suggest mistakes are more likely to be persistent when they are driven by incorrect mental models that miss or misrepresent important aspects of the environment. Such models induce confidence in initial answers, limiting engagement with and learning from feedback. We substantiate these insights in an alternative scenario where individuals involved in a voting problem overlook the importance of being pivotal.