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dc.contributor.authorAubin, Jean-Pierre
dc.date.accessioned2011-06-07T10:19:21Z
dc.date.available2011-06-07T10:19:21Z
dc.date.issued2005
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6440
dc.language.isoenen
dc.subjectHamilton-Jacobi-Isaacs partial differential equationen
dc.subjectfuzzy coalitionsen
dc.subjectdynamic coreen
dc.subjectdynamic cooperative gameen
dc.subject.ddc519en
dc.titleDynamic Core of Fuzzy Dynamical Cooperative Gamesen
dc.typeChapitre d'ouvrage
dc.description.abstractenWe use in this paper the viability/capturability approach for studying the problem of characterizing the dynamic core of a dynamic cooperative game defined in a characteristic function form. In order to allow coalitions to evolve, we embed them in the set of fuzzy coalitions. Hence, we define the dynamic core as a set-valued map associating with each fuzzy coalition and each time the set of allotments is such that their payoffs at that time to the fuzzy coalition are larger than or equal to the one assigned by the characteristic function of the game. We shall characterize this core through the (generalized) derivatives of a valuation function associated with the game. We shall provide its explicit formula, characterize its epigraph as a viable-capture basin of the epigraph of the characteristic function of the fuzzy dynamical cooperative game, use the tangential properties of such basins for proving that the valuation function is a solution to a Hamilton-Jacobi-Isaacs partial differential equation and use this function and its derivatives for characterizing the dynamic core.en
dc.identifier.citationpages129-162en
dc.relation.ispartofseriestitleAnnals of the International Society of Dynamic Games
dc.relation.ispartofseriesnumber7
dc.relation.ispartoftitleAdvances in Dynamic Games. Applications to Economics, Finance, Optimization, and Stochastic Controlen
dc.relation.ispartofeditorNowak, Andrzej
dc.relation.ispartofeditorSzajowski, Krzysztof
dc.relation.ispartofpublnameSpringeren
dc.relation.ispartofpublcityBerlinen
dc.relation.ispartofdate2005
dc.relation.ispartofpages679en
dc.relation.ispartofurlhttp://dx.doi.org/10.1007/b138903en
dc.description.sponsorshipprivateouien
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.ispartofisbn978-0-8176-4362-1en
dc.identifier.doihttp://dx.doi.org/10.1007/0-8176-4429-6_7


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