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Inertial Game Dynamics and Applications to Constrained Optimization

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.identifierLaboratoire d'Informatique de Grenoble [LIG]
dc.contributor.authorMertikopoulos, Panayotis
HAL ID: 1933
ORCID: 0000-0003-2026-9616
dc.date.accessioned2017-03-06T13:58:10Z
dc.date.available2017-03-06T13:58:10Z
dc.date.issued2015
dc.identifier.issn0363-0129
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/16290
dc.language.isoenen
dc.subjectGame dynamicsen
dc.subjectfolk theoremen
dc.subjectHessian–Riemannian metricsen
dc.subjectlearningen
dc.subjectreplicator dynamicsen
dc.subjectsecond-order dynamicsen
dc.subjectstability of equilibriaen
dc.subjectwell-posednessen
dc.subject.ddc519en
dc.subject.classificationjelC.C7.C79en
dc.titleInertial Game Dynamics and Applications to Constrained Optimizationen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenAiming to provide a new class of game dynamics with good long-term convergence properties, we derive a second-order inertial system that builds on the widely studied “heavy ball with friction” optimization method. By exploiting a well-known link between the replicator dynamics and the Shahshahani geometry on the space of mixed strategies, the dynamics are stated in a Riemannian geometric framework where trajectories are accelerated by the players' unilateral payoff gradients and they slow down near Nash equilibria. Surprisingly (and in stark contrast to another second-order variant of the replicator dynamics), the inertial replicator dynamics are not well-posed; on the other hand, it is possible to obtain a well-posed system by endowing the mixed strategy space with a different Hessian--Riemannian (HR) metric structure, and we characterize those HR geometries that do so. In the single-agent version of the dynamics (corresponding to constrained optimization over simplex-like objects), we show that regular maximum points of smooth functions attract all nearby solution orbits with low initial speed. More generally, we establish an inertial variant of the so-called folk theorem of evolutionary game theory, and we show that strict equilibria are attracting in asymmetric (multipopulation) games, provided, of course, that the dynamics are well-posed. A similar asymptotic stability result is obtained for evolutionarily stable states in symmetric (single-population) games.en
dc.relation.isversionofjnlnameSIAM Journal on Control and Optimization
dc.relation.isversionofjnlvol53en
dc.relation.isversionofjnlissue5en
dc.relation.isversionofjnldate2015-10
dc.relation.isversionofjnlpages3141-3170en
dc.relation.isversionofdoi10.1137/130920253en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidateouien
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2017-03-06T13:30:36Z
hal.identifierhal-01483807*
hal.version1*
hal.update.actionupdateFiles*
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