  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.
