Limit Points of Endogenous Misspecified Learning

Abstract

We study how an agent learns from endogenous data when their prior belief is misspecified. We show that only \emph{uniform Berk-Nash equilibria} can be long-run outcomes and that all \emph{uniformly strict Berk-Nash equilibria} have an arbitrarily high probability of being the long-run outcome for some initial beliefs. When the agent believes the outcome distribution is exogenous, every uniformly strict Berk-Nash equilibrium has a positive probability of being the long-run outcome for any initial belief. We generalize these results to settings where the agent observes a signal before acting.

Keywords: Misspecified Learning, Berk-Nash Equilibrium