  We consider two classes of constrained finite state-action stochastic games.
First, we consider a two player nonzero sum single controller constrained
stochastic game with both average and discounted cost criterion. We consider
the same type of constraints as in [1], i.e., player 1 has subscription based
constraints and player 2, who controls the transition probabilities, has
realization based constraints which can also depend on the strategies of player
1. Next, we consider a N -player nonzero sum constrained stochastic game with
independent state processes where each player has average cost criterion as
discussed in [2]. We show that the stationary Nash equilibria of both classes
of constrained games, which exists under strong Slater and irreducibility
conditions [3], [2], has one to one correspondence with global minima of
certain mathematical programs. In the single controller game if the constraints
of player 2 do not depend on the strategies of the player 1, then the
mathematical program reduces to the non-convex quadratic program. In two player
independent state processes stochastic game if the constraints of a player do
not depend on the strategies of another player, then the mathematical program
reduces to a non-convex quadratic program. Computational algorithms for finding
global minima of non-convex quadratic program exist [4], [5] and hence, one can
compute Nash equilibria of these constrained stochastic games. Our results
generalize some existing results for zero sum games [1], [6], [7].
