Nonzero-sum games for continuous-time Markov chains with unbounded transition and average payoff rates

Abstract

This paper attempts to study two-person nonzero-sum games for denumerable continuous-time Markov chains determined by transition rates, with an expected average criterion. The transition rates are allowed to be unbounded, and the payoff functions may be unbounded from above and from below. We give suitable conditions under which the existence of a Nash equilibrium is ensured. More precisely, using the socalled “vanishing discount” approach, a Nash equilibrium for the average criterion is obtained as a limit point of a sequence of equilibrium strategies for the discounted criterion as the discount factors tend to zero. Our results are illustrated with a birth-and-death game.