Berk-Nash Equilibrium: A Framework for Modeling Agents with Misspecified Models

TL;DR

This paper introduces Berk-Nash equilibrium, a new framework modeling agents with potentially misspecified beliefs, where beliefs are chosen to best fit observed outcomes using Kullback-Leibler divergence, extending classical equilibrium concepts.

Contribution

It formalizes Berk-Nash equilibrium, integrating misspecified beliefs into game theory and providing a learning foundation that generalizes Nash and self-confirming equilibria.

Findings

Berk-Nash equilibrium accounts for agents with incorrect models.

Beliefs are updated to best fit observed data via KL divergence.

Framework unifies and extends existing equilibrium concepts.

Abstract

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.