Discrete-time zero-sum Markov games with first passage criteria. (3rd April 2017)

• Record Type: Journal Article
• Authors: Liu, Qiuli; Huang, Xiangxiang
• Is Part Of: Optimization. Volume 66:Number 4(2017)
• Page Start: 571
• Page End: 587
• Publication Date: 2017-04-03
• Subjects: Zero-sum stochastic games -- state-dependent -- discount payoff -- first passage time -- optimal policy; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1278001
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we deal with two-person zero-sum stochastic games for discrete-time Markov processes. The optimality criterion to be studied is the discounted payoff criterion during a first passage time to some target set, where the discount factor is state-dependent. The state and action spaces are all Borel spaces, and the payoff functions are allowed to be unbounded. Under the suitable conditions, we first establish the optimality equation. Then, using dynamic programming techniques, we obtain the existence of the value of the game and a pair of optimal stationary policies. Moreover, we present the exponential convergence of the value iteration and a 'martingale characterization' of a pair of optimal policies. Finally, we illustrate the applications of our main results with an inventory system.