Zero-sum Markov games with impulse controls

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buir.contributor.authorBasu, Arnab
dc.citation.epage604en_US
dc.citation.issueNumber1en_US
dc.citation.spage580en_US
dc.citation.volumeNumber58en_US
dc.contributor.authorBasu, Arnab
dc.contributor.authorStettner, L.
dc.date.accessioned2021-03-31T03:00:41Z
dc.date.available2021-03-31T03:00:41Z
dc.date.issued2020
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractIn this paper we consider a zero-sum Markov stopping game on a general state space with impulse strategies and infinite time horizon discounted payoff where the state dynamics is a weak Feller--Markov process. One of the key contributions is our analysis of this problem based on “shifted” strategies, thereby proving that the original game can be practically restricted to a sequence of Dynkin's stopping games without affecting the optimalty of the saddle-point equilibria and hence completely solving some open problems in the existing literature. Under two quite general (weak) assumptions, we show the existence of the value of the game and the form of saddle-point (optimal) equilibria in the set of shifted strategies. Moreover, our methodology is different from the previous techniques used in the existing literature and is based on purely probabilistic arguments. In the process, we establish an interesting property of the underlying Feller--Markov process and the impossibility of infinite number of impulses in finite time under saddle-point strategies which is crucial for the verification result of the corresponding Isaacs--Bellman equations.en_US
dc.identifier.doi10.1137/18M1229365en_US
dc.identifier.eissn1095-7138
dc.identifier.issn0363-0129
dc.identifier.urihttp://hdl.handle.net/11693/76033
dc.language.isoEnglishen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.relation.isversionofhttps://doi.org/10.1137/18M1229365en_US
dc.source.titleSIAM Journal on Control and Optimizationen_US
dc.subjectFeller–Markov processesen_US
dc.subjectStopping timesen_US
dc.subjectZero-sum gamesen_US
dc.subjectIsaacs–Bellman equationsen_US
dc.subjectDynkin’s stopping gameen_US
dc.subjectImpulse controlsen_US
dc.subjectSaddle-point strategiesen_US
dc.subjectDiscounted costen_US
dc.titleZero-sum Markov games with impulse controlsen_US
dc.typeArticleen_US
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