A Tauberian Theorem for Nonexpansive Operators and Applications to Zero-Sum Stochastic Games

• 成果类型: Article
• 署名作者: Ziliotto, Bruno
• 署名单位: Universite PSL; Universite Paris-Dauphine
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2016.0788
• 发表日期: 2016
• 页码: 1522-1534
• 关键词: markov-chain games; incomplete information; Absorbing games; EXISTENCE; strategies

摘要

We prove a Tauberian theorem for nonexpansive operators and apply it to the model of zero-sum stochastic game. Under mild assumptions, we prove that the value of the lambda-discounted game converges uniformly when lambda goes to zero if and only if the value of the n-stage game converges uniformly when n goes to infinity. This generalizes the Tauberian theorem of Lehrer and Sorin [Lehrer E, Sorin S (1992) A uniform Tauberian theorem in dynamic programming. Math. Oper. Res. 17(2): 303-307] to the two-player zero-sum case. We also provide the first example of a stochastic game with public signals on the state and perfect observation of actions, with finite state space, signal sets, and action sets, in which for some initial state known by both players, the value of the lambda-discounted game and the value of the n-stage game starting at that initial state converge to distinct limits.