Nash equilibria for total expected reward absorbing Markov games: the constrained and unconstrained cases

2023/05/08 by François Dufour, Dufour, François, Tomás Prieto-Rumeau +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Mathematics #Game Theory and Applications #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2305.04514

openalex publication_date 2023/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider a nonzero-sum N-player Markov game on an abstract measurable state space with compact metric action spaces. The payoff functions are bounded Carathéodory functions and the transitions of the system are assumed to have a density function satisfying some continuity conditions. The optimality criterion of the players is given by a total expected payoff on an infinite discrete-time horizon. Under the condition that the game model is absorbing, we establish the existence of Markov strategies that are a noncooperative equilibrium in the family of all history-dependent strategies of the players for both the constrained and the unconstrained problems, We obtain, as a particular case of results, the existence of Nash equilibria for discounted constrained and unconstrained game models.

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• On characterization and existence of constrained correlated equilibria in Markov games

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