Zero-Sum Games for Finite-Horizon Semi-Markov Processes Under the Probability Criterion

• 成果类型: Article
• 署名作者: Huang, Xiangxiang; Guo, Xianping; Wen, Xin
• 署名单位: Dongguan University of Technology; Sun Yat Sen University; Sun Yat Sen University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3220507
• 发表日期: 2023
• 页码: 5560-5567
• 关键词: games; game theory; Markov processes; kernel; iterative methods; COSTS; Heuristic algorithms; Finite-horizon semi-Markov process; probability criterion; saddle point; value iterative algorithm; Zero-sum game

摘要

This study discusses a two-person zero-sum game for finite-horizon semi-Markov processes, where the concerned criterion is the probability that the total payoff produced by a system during a finite horizon exceeds a prescribed goal. We establish the Shapley equation and the existence of a saddle point under a suitable condition. Moreover, we develop a value iterative algorithm to compute an e-saddle point and approach the value of the game by solving a series of matrix games. The construction of the e-saddle point and the convergence of the algorithm are also shown. Finally, we demonstrate the application of our main results by an example on an inventory system.