Stationary Markov Nash equilibria for nonzero-sum constrained ARAT Markov games
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]
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]
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]
< Reduce
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]
Language
en
Article de revue
This item was published in
SIAM Journal on Control and Optimization. 2022
Society for Industrial and Applied Mathematics
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Nash equilibrium
Nonzero-sum games
Constrained games
ARAT games
Origin
Hal imported