Extremal Shift Rule for Continuous-Time Zero-Sum Markov Games

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• 作者：Yurii Averboukh
• 关键词：Continuous ; time Markov games ; Differential games ; Extremal shift rule ; Control with guide strategies
• 刊名：Dynamic Games and Applications
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：7
• 期：1
• 页码：1-20
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Game Theory, Economics, Social and Behav. Sciences; Economic Theory/Quantitative Economics/Mathematical Methods; Operations Research, Management Science; Economics, general; Communications Engineering
• 出版者：Springer US
• ISSN：2153-0793
• 卷排序：7

文摘

In the paper we consider the controlled continuous-time Markov chain describing the interacting particles system with the finite number of types. The system is controlled by two players with the opposite purposes. This Markov game converges to a zero-sum differential game when the number of particles tends to infinity. Krasovskii–Subbotin extremal shift provides the optimal strategy in the limiting game. The main result of the paper is the near optimality of the Krasovskii–Subbotin extremal shift rule for the original Markov game.