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

We consider a two-person zero-sum continuous-time Markov game GG 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 GG we construct finite state and actions game models GnGn whose value functions converge to the value of GG. Rates of convergence are given. We propose a policy iteration algorithm for the finite state and actions games GnGn. We show an application to a population system.