Zero-sum stochastic games with average payoffs: new optimality conditions
This paper is devoted to the study of zero-sum Markov games on a countable state space. The authors provide conditions that assure the existence of a value of the game and optimal strategies for both players when the average expected payoff criterion is used. This purpose is achieved by establishing the optimality equation via discounted games. The key assumption in the analysis is the following one: the relative difference of the discounted value is bounded from above and below by a function of a finite weighted norm. This requirement is well-known within a dynamic programming framework and has been extensively used in MDP mdels, see, e.g., \textit{L. I. Sennott} [Stochastic dynamic programming and the control of queueing systems, New York, Wiley (1999; Zbl 0997.93503)], Chapter 7.7 or a recent paper of \textit{X. Guo} and \textit{Q Zhu} [J. Appl. Probab. 43, No. 2, 318--334 (2006; Zbl 1121.90122)].
scientific article; zbMATH DE number 5601616
scientific article