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We consider a zero-sum stochastic game with side constraints for both players with a special structure. There are two independent con- trolled Markov chains, one for each player. The transition probabilities of the chain associated with a player as well as the related side constraints depend only on the actions of the corresponding player; the side constraints also depend on the player's controlled chain. The global cost that player 1 wishes to minimize and that player 2 wishes to maximize, depend however on the actions and Markov chains of both players. We obtain a linear pro- gramming (LP) formulations that allows to compute the value and saddle point policies for this problem. We illustrate the theoretical results through a zero-sum stochastic game in wireless networks in which each player has power constraints.

Zero-sum constrained stochastic games with independent state processes