Polynomial stochastic games via sum of squares optimization

Stochastic games are an important class of games that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards. The players are assumed to have infinite strategy spaces and the payoffs are assumed to be polynomials. In this paper we restrict our attention to a very special class of games for which the single-controller assumption holds. It is shown that minimax equilibria and optimal strategies for such games may be obtained via semidefinite programming.