Approximation of two-person zero-sum continuous-time Markov games with average payoff criterion

Abstract

We consider a two-person zero-sum continuous-time Markov game G with denumerable state space, Borel action spaces, unbounded payoff and transition rates, under the long-run expected average payoff criterion. To approximate numerically the value of G we construct finite state and actions game models Gn whose value functions converge to the value of G. Rates of convergence are given. We propose a policy iteration algorithm for the finite state and actions games Gn. We show an application to a population system.