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hal.structure.identifierLaboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
dc.contributor.authorLaraki, Rida
HAL ID: 179670
ORCID: 0000-0002-4898-2424
hal.structure.identifier
dc.contributor.authorRenault, Jérôme
HAL ID: 21086
dc.date.accessioned2020-11-18T09:29:42Z
dc.date.available2020-11-18T09:29:42Z
dc.date.issued2017
dc.identifier.issn0364-765X
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/21209
dc.language.isoenen
dc.subjectMarkov Decision Processesen
dc.subjectZero-Sum Stochastic Gamesen
dc.subjectAsymptotic Valueen
dc.subjectGambling Housesen
dc.subjectMertens-Zamir Systemen
dc.subjectSplitting Gamesen
dc.subjectPersuasionen
dc.subject.ddc519en
dc.titleAcyclic Gambling Gameen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider 2-player zero-sum stochastic games where each player controls his own state variable living in a compact metric space. The terminology comes from gambling problems where the state of a player represents its wealth in a casino. Under natural assumptions (such as continuous running payoff and non expansive transitions), we consider for each discount factor the value vλ of the λ-discounted stochastic game and investigate its limit when λ goes to 0 (players are more and more patient). We show that under a new acyclicity condition, the limit exists and is characterized as the unique solution of a system of functional equations: the limit is the unique continuous excessive and depressive function such that each player, if his opponent does not move, can reach the zone when the current payoff is at least as good than the limit value, without degrading the limit value. The approach generalizes and provides a new viewpoint on the Mertens-Zamir system coming from the study of zero-sum repeated games with lack of information on both sides. A counterexample shows that under a slightly weaker notion of acyclicity, convergence of (vλ) may fail.en
dc.relation.isversionofjnlnameMathematics of Operations Research
dc.relation.isversionofjnlvol45en
dc.relation.isversionofjnlissue4en
dc.relation.isversionofjnldate2020-11
dc.relation.isversionofjnlpages1193-1620en
dc.relation.isversionofdoi10.2139/ssrn.3187425en
dc.relation.isversionofjnlpublisherINFORMSen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2020-11-18T09:25:13Z
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