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hal.structure.identifierDepartment of Economics Columbia University
dc.contributor.authorBarilla, César
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorCarlier, Guillaume
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorLasry, Jean-Michel
dc.date.accessioned2021-11-23T12:38:25Z
dc.date.available2021-11-23T12:38:25Z
dc.date.issued2021
dc.identifier.issn2164-6066
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22218
dc.language.isoenen
dc.subjectIterative Proportional Fitting procedure (IPFP)en
dc.subjectLabour market equilibriumen
dc.subjectConvex dualityen
dc.subjectOptimal transporten
dc.subjectMean field gamesen
dc.subject.ddc515en
dc.titleA mean field game model for the evolution of citiesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe propose a (toy) MFG model for the evolution of residents and firms densities, coupled both by labour market equilibrium conditions and competition for land use (congestion). This results in a system of two Hamilton-Jacobi-Bellman and two Fokker-Planck equations with a new form of coupling related to optimal transport. This MFG has a convex potential which enables us to find weak solutions by a variational approach. In the case of quadratic Hamiltonians, the problem can be reformulated in Lagrangian terms and solved numerically by an IPFP/Sinkhorn-like scheme as in [4]. We present numerical results based on this approach, these simulations exhibit different behaviours with either agglomeration or segregation dominating depending on the initial conditions and parameters.en
dc.relation.isversionofjnlnameJournal of Dynamics and Games
dc.relation.isversionofjnlvol8en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2021-07
dc.relation.isversionofjnlpages299-329en
dc.relation.isversionofdoi10.3934/jdg.2021017en
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-03086616en
dc.relation.isversionofjnlpublisherAIMS - American Institute of Mathematical Sciencesen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2021-11-23T12:35:11Z
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