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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorClaisse, Julien
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorRen, Zhenjie
hal.structure.identifierDepartment of Mathematics [CUHK]
dc.contributor.authorTan, Xiaolu
dc.date.accessioned2021-09-15T12:00:40Z
dc.date.available2021-09-15T12:00:40Z
dc.date.issued2019-12
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/21775
dc.language.isoenen
dc.subjectMean field gamesen
dc.subjectbranching diffusion processen
dc.subjectrelaxed controlen
dc.subject.ddc519en
dc.titleMean field games with branchingen
dc.typeDocument de travail / Working paper
dc.description.abstractenMean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout the game. However, in various applications, such as population dynamics or economic growth, the number of players can vary across time which may lead to different Nash equilibria. For this reason, we introduce a branching mechanism in the population of agents and obtain a variation on the mean field game problem. As a first step, we study a simple model using a PDE approach to illustrate the main differences with the classical setting. We prove existence of a solution and show that it provides an approximate Nash-equilibrium for large population games. We also present a numerical example for a linear--quadratic model. Then we study the problem in a general setting by a probabilistic approach. It is based upon the relaxed formulation of stochastic control problems which allows us to obtain a general existence result.en
dc.identifier.citationpages32en
dc.relation.ispartofseriestitleCahier de recherche CEREMADEen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenon
dc.description.halcandidateouien
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2021-09-15T11:31:41Z
hal.identifierhal-03345264
hal.version1
hal.date.transferred2021-09-15T12:00:42Z
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