Repeated games with incomplete information on one side: The case of different discount factors

Two players engage in a repeated game with incomplete information on one side, where the underlying stage-games are zero-sum. In the case where players evaluate their stage-payoffs by using different discount factors, the payoffs of the infinitely repeated game are typically non zero-sum. However, if players grow infinitely patient, then the equilibrium payoffs will sometimes approach the zero-sum result, depending on the asymptotic relative patience of the players. We provide sufficient conditions that ensure a zero-sum limit. Moreover, we provide examples of games violating these conditions that possess `cooperative' equilibria whose payoffs are bounded away from the zero-sum payoffs set.