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dc.contributor.authorVigeral, Guillaume
dc.contributor.authorBolte, Jérôme
dc.contributor.authorGaubert, Stéphane
dc.date.accessioned2014-01-22T15:28:56Z
dc.date.available2014-01-22T15:28:56Z
dc.date.issued2014
dc.identifier.issn0364-765X
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/12487
dc.language.isoenen
dc.subjectuniform value,
dc.subjectnonlinear Perron-Frobenius theory
dc.subjectrisk-sensitive control
dc.subjecto-minimal structures
dc.subjecttropical geometry
dc.subjectnonexpansive mappings
dc.subjectdefinable games
dc.subjectShapley operator
dc.subjectZero-sum stochastic game
dc.subject.ddc519en
dc.titleDefinable zero-sum stochastic games
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherMAXPLUS (INRIA Saclay - Ile de France) INRIA – CNRS : UMR – Polytechnique -;France
dc.contributor.editoruniversityotherCentre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) http://www.cmap.polytechnique.fr/ Polytechnique - X – CNRS : UMR7641;France
dc.contributor.editoruniversityotherGroupe de recherche en économie mathématique et quantitative (GREMAQ) http://www-gremaq.univ-tlse1.fr/ CNRS : UMR5604 – Université des Sciences Sociales - Toulouse I – École des Hautes Études en Sciences Sociales (EHESS) – Institut national de la recherche agronomique (INRA) : UMR;France
dc.description.abstractenDefinable zero-sum stochastic games involve a finite number of states and action sets, reward and transition functions that are definable in an o-minimal structure. Prominent examples of such games are finite, semi-algebraic or globally subanalytic stochastic games. We prove that the Shapley operator of any definable stochastic game with separable transition and reward functions is definable in the same structure. Definability in the same structure does not hold systematically: we provide a counterexample of a stochastic game with semi-algebraic data yielding a non semi-algebraic but globally subanalytic Shapley operator. %Showing the definability of the Shapley operator in full generality appears thus as a complex and challenging issue. } Our definability results on Shapley operators are used to prove that any separable definable game has a uniform value; in the case of polynomially bounded structures we also provide convergence rates. Using an approximation procedure, we actually establish that general zero-sum games with separable definable transition functions have a uniform value. These results highlight the key role played by the tame structure of transition functions. As particular cases of our main results, we obtain that stochastic games with polynomial transitions, definable games with finite actions on one side, definable games with perfect information or switching controls have a uniform value. Applications to nonlinear maps arising in risk sensitive control and Perron-Frobenius theory are also given.
dc.relation.isversionofjnlnameMathematics of Operations Research
dc.relation.isversionofjnldate2014
dc.relation.isversionofdoihttp://dx.doi.org/10.1287/moor.2014.0666
dc.relation.isversionofjnlpublisherInstitute of Management Sciences
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingprintoui
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2016-05-30T13:47:58Z


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