DUFOUR, François; PRIETO-RUMEAU, Tomás

doi:10.1137/21M144565X

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DUFOUR, François
Méthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Institut Polytechnique de Bordeaux [Bordeaux INP]

PRIETO-RUMEAU, Tomás
Universidad Estatal a Distancia [UNED]

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SIAM Journal on Control and Optimization. 2022

Society for Industrial and Applied Mathematics

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We consider a nonzero-sum Markov game on an abstract measurable state space with compact metric action spaces. The goal of each player is to maximize his respective discounted payoff function under the condition that some constraints on a discounted payoff are satisfied. We are interested in the existence of a Nash or noncooperative equilibrium. Under suitable conditions, which include absolute continuity of the transitions with respect to some reference probability measure, additivity of the payoffs and the transition probabilities (ARAT condition), and continuity in action of the payoff functions and the density function of the transitions of the system, we establish the existence of a constrained stationary Markov Nash equilibrium, that is, the existence of stationary Markov strategies for each of the players yielding an optimal profile within the class of all history-dependent profiles.< Réduire

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Nash equilibrium

Nonzero-sum games

Constrained games

ARAT games

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

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