Tauberian theorems for general iterations of operators: 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; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2018.01.009
• 发表日期: 2018
• 页码: 486-503
• 关键词: Tauberian theorem; Nonexpansive operators; stochastic games; Asymptotic value; Weighted payoffs

摘要

This paper proves several Tauberian theorems for general iterations of operators, and provides two applications to zero-sum stochastic games where the total payoff is a weighted sum of the stage payoffs. The first application is to provide conditions under which the existence of the asymptotic value implies the convergence of the values of the weighted game, as players get more and more patient. The second application concerns stochastic games with finite state space and action sets. This paper builds a simple class of asymptotically optimal strategies in the weighted game, that at each stage play optimally in a discounted game with a discount factor corresponding to the relative weight of the current stage. (C) 2018 Elsevier Inc. All rights reserved.