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

Yurii Averboukh ()
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Yurii Averboukh: Krasovskii Institute of Mathematics and Mechanics UrB RAS

Dynamic Games and Applications, 2017, vol. 7, issue 1, No 1, 20 pages

Abstract: Abstract 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.

Keywords: Continuous-time Markov games; Differential games; Extremal shift rule; Control with guide strategies; 91A15; 91A23; 91A05 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13235-015-0173-z

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