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We consider two classes of constrained finite state-action stochastic games.First, we consider a two player nonzero sum single controller constrainedstochastic game with both average and discounted cost criterion. We considerthe same type of constraints as in [1], i.e., player 1 has subscription basedconstraints and player 2, who controls the transition probabilities, hasrealization based constraints which can also depend on the strategies of player1. Next, we consider a N -player nonzero sum constrained stochastic game withindependent state processes where each player has average cost criterion asdiscussed in [2]. We show that the stationary Nash equilibria of both classesof constrained games, which exists under strong Slater and irreducibilityconditions [3], [2], has one to one correspondence with global minima ofcertain mathematical programs. In the single controller game if the constraintsof player 2 do not depend on the strategies of the player 1, then themathematical program reduces to the non-convex quadratic program. In two playerindependent state processes stochastic game if the constraints of a player donot depend on the strategies of another player, then the mathematical programreduces to a non-convex quadratic program. Computational algorithms for findingglobal minima of non-convex quadratic program exist [4], [5] and hence, one cancompute Nash equilibria of these constrained stochastic games. Our resultsgeneralize some existing results for zero sum games [1], [6], [7].

A mathematical programming based characterization of Nash equilibria of some constrained stochastic games