  Stochastic games are an important class of problems 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 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.
