Perturbed zero-sum games with applications to stochastic and repeated games

This paper deals with perturbed matrix games. The main result is that for a large class of perturbations, the sets of solutions of perturbed games converge to subsets of solutions of appropriate lexicographic games. We consider applications of these results to dynamic games with finite numbers of states. In particular, we apply our main result to the following three models: (i) infinite-horizon stochastic games with perturbed transition probabilities and rewards when only one player controls transition probabilities; (ii) finite-horizon stochastic games with perturbed transition probabilities and rewards when both players control transition probabilities; and (iii) repeated games with weighted discounted criteria.