The possibility of Bayesian learning in repeated games

In infinitely repeated games, Nachbar (1997, 2005) has shown that Bayesian learning of a restricted strategy set is inconsistent; the beliefs required to learn any element of such a set will lead best responses to lie outside of it in most games. But I establish here that Nash convergence of Bayesian learning requires only that optimal play (rather than any possible play) is learnable, and an appropriately modified notion of learnability is consistent in many of the games to which Nachbar's result applies. This means that rational learning of equilibrium is possible in an important class including coordination games, which I illustrate with two examples of positive learning results