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We consider a nonzero-sum Markov game on an abstract measurable state spacewith compact metric action spaces. The goal of each player is to maximize hisrespective discounted payoff function under the condition that some constraintson a discounted payoff are satisfied. We are interested in the existence of aNash or noncooperative equilibrium. Under suitable conditions, which includeabsolute continuity of the transitions with respect to some referenceprobability measure, additivity of the payoffs and the transition probabilities(ARAT condition), and continuity in action of the payoff functions and thedensity function of the transitions of the system, we establish the existenceof a constrained stationary Markov Nash equilibrium, that is, the existence ofstationary Markov strategies for each of the players yielding an optimalprofile within the class of all history-dependent profiles.

Stationary Markov Nash equilibria for nonzero-sum constrained ARAT Markov games