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

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].


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