Berk-Nash Rationalizability

We introduce Berk--Nash rationalizability, a set-valued counterpart to Berk--Nash equilibrium for environments in which agents may hold misspecified models. A set of behaviors is self-justified if every behavior in the set is optimal under beliefs fitted to data generated within the set. Berk--Nash rationalizability is the largest self-justified set and reduces to standard rationalizability under correct specification and identification. We provide a learning foundation allowing Bayesian agents to learn from different, selectively sampled histories: almost surely, the limit set of play is self-justified. Conversely, under identification, any compact self-justified set can arise as the limit set with arbitrarily high probability. We illustrate how the concept yields informative predictions that are robust across learning procedures, without committing to a specific dynamic or assuming convergence.