Zero-Sum Discounted Reward Criterion Games for Piecewise Deterministic Markov Processes

Abstract : This papers dealswith the zero-sum gamewith a discounted reward criterion for piecewise deterministic Markov process (PDMPs) in general Borel spaces. The two players can act on the jump rate and transition measure of the process, with the decisions being taken just after a jump of the process. The goal of this paper is to derive conditions for the existence of min–max strategies for the infinite horizon total expected discounted reward function, which is composed of running and boundary parts. The basic idea is, by using the special features of the PDMPs, to re-write the problem via an embedded discrete-time Markov chain associated to the PDMP and re-formulate the problem as a discrete-stage zero sum game problem.
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Submitted on : Tuesday, November 21, 2017 - 8:44:55 AM
Last modification on : Friday, December 14, 2018 - 1:17:11 AM

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Oswaldo Luiz Do Valle Costa, François Dufour. Zero-Sum Discounted Reward Criterion Games for Piecewise Deterministic Markov Processes. Applied Mathematics and Optimization, Springer Verlag (Germany), 2018, ⟨10.1007/s00245-017-9416-2⟩. ⟨hal-01643056⟩

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