Undiscounted two-person zero-sum communicating stochastic games

Consider two-person zero-sum communicating stochastic games with finite state and finite action spaces under the long-run average payoff criterion. A communicating game is irreducible on a restricted strategy space where every pair of action is taken with positive probability. The proposed approach applies Hoffman and Karp's (1996) algorithm for irreducible games successively over a sequence of restricted strategy spaces that gets larger until an /spl epsiv/-optimal stationary policy pair is obtained for any /spl epsiv/>0. This algorithm is convergent for the games that have optimal strategies with a value independent of the initial state.