An Equilibrium Framework for Players with Misspecified Models

We introduce an equilibrium framework that relaxes the standard assumption that people have a correctly-specified view of their environment. Players repeatedly play a simultaneous-move game where they potentially face both strategic and payoff uncertainty. Each player has a potentially misspecified view of the environment and uses Bayes' rule to update her views based on the (possibly partial) feedback obtained at the end of each period. We show that steady-state behavior of this multi-player decision and learning problem is captured by a generalized notion of equilibrium: a strategy profile such that each player optimizes given certain beliefs and where these beliefs put probability one on those subjective distributions over consequences that are closest---in terms of relative entropy---to the correct, equilibrium distribution. 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.