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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorCardaliaguet, Pierre
hal.structure.identifierLaboratoire Jean Alexandre Dieudonné [JAD]
dc.contributor.authorDelarue, François
HAL ID: 8630
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorLasry, Jean-Michel
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorLions, Pierre-Louis
dc.subjectmean field gamesen
dc.titleThe master equation and the convergence problem in mean field gamesen
dc.typeDocument de travail / Working paper
dc.description.abstractenThe paper studies the convergence, as N tends to infinity, of a system of N coupled Hamilton-Jacobi equations, the Nash system. This system arises in differential game theory. We describe the limit problem in terms of the so-called master equation " , a kind of second order partial differential equation stated on the space of probability measures. Our first main result is the well-posedness of the master equation. To do so, we first show the existence and uniqueness of a solution to the " mean field game system with common noise " , which consists in a coupled system made of a backward stochastic Hamilton-Jacobi equation and a forward stochastic Kolmogorov equation and which plays the role of characteristics for the master equation. Our second main result is the convergence, in average, of the solution of the Nash system and a propagation of chaos property for the associated " optimal trajectories " ."en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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