Constrained Markov games: Nash equilibria. (English) Zbl 0957.91014

Altman, Eitan; Shwartz, Adam

Filar, Jerzy A. (ed.) et al., Advances in dynamic games and applications. Proceedings of the 7th international symposium, Kanagawa, Japan, December 16-18, 1996. Boston: Birkhäuser. Ann. Int. Soc. Dyn. Games. 5, 213-221 (2000).

Summary: The authors develop the theory of constrained Markov games. They consider the expected average cost as well as discounted cost. They allow different players to have different types of costs. They present sufficient conditions for the existence of stationary Nash equilibrium. The results are based on the theory of sensitivity analysis of mathematical programs developed by G. B. Dantzig, J. Folkman and N. Shapiro [J. Math. Anal. Appl.17, 519-548 (1967; Zbl 0153.49201]e)], which was applied to Markov Decision Processes (MDPs) [in E. Altman and A. Shwartz, Ann. Oper. Res. 32, 1-22 (1991; Zbl 0735.60091)]. They further characterize all stationary Nash equilibria as fixed points of some coupled linear programs.
For the entire collection see [Zbl 0938.00018].

MSC:

91A15	Stochastic games, stochastic differential games
90C40	Markov and semi-Markov decision processes

Keywords:

constrained Markov games; expected average cost; discounted cost; stationary Nash equilibrium; sensitivity analysis; stationary Nash equilibria

Citations:

Zbl 0735.60091; Zbl 0153.49201