A limit theorem for equilibria under ambiguous belief correspondences.

Previous literature shows that, in many different models, limits of equilibria of perturbed games are equilibria of the unperturbed game when the sequence of perturbed games converges to the unperturbed one in an appropriate sense. The question of whether such a limit property extends to the equilibrium notions in ambiguous games is not yet as clear as it seems; in fact, previous literature shows that the extension fails in simple examples.