A characterization of stationary Nash equilibria of constrained stochastic games with independent state processes

We characterize the stationary Nash equilibria of a N-player general sum constrained stochastic game with independent state processes studied in Altman et al. (2008), via the global minimizers of a certain non-convex mathematical program. We identify a subclass of these N-player general sum games called Additive Cost-Decoupled Constraints Cost games for which the above characterization is via linear programs. The linear programs for two player zero sum games as given in Altman et al. (2005) can be obtained as a special case of our mathematical program.