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.