  We introduce an evolutionary framework to evaluate competing
(mis)specifications in strategic situations, focusing on which
misspecifications can persist over a correct specification. Agents with
heterogeneous specifications coexist in a society and repeatedly match against
random opponents to play a stage game. They draw Bayesian inferences about the
environment based on personal experience, so their learning depends on the
distribution of specifications and matching assortativity in the society. One
specification is evolutionarily stable against another if, whenever
sufficiently prevalent, its adherents obtain higher expected objective payoffs
than their counterparts. The learning channel leads to novel stability
phenomena compared to frameworks where the heritable unit of cultural
transmission is a single belief instead of a specification (i.e., set of
feasible beliefs). We apply the framework to linear-quadratic-normal games
where players receive correlated signals but possibly misperceive the
information structure. The correct specification is not evolutionarily stable
against a correlational error, whose direction depends on matching
assortativity. As another application, the framework also endogenizes coarse
analogy classes in centipede games.
