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Documents  35Q91 | enregistrements trouvés : 5

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- ix; 307 p.
ISBN 978-0-8218-8736-3

Contemporary mathematics , 0594

Localisation : Collection 1er étage

équation différentielle non linéaire # équation différentielle parabolique

35-06 ; 34-06 ; 35K55 ; 35L70 ; 47-06 ; 58-06 ; 35Q91 ; 00B25 ; 00B30

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Research schools;Partial Differential Equations;Mathematics in Science and Technology

We propose a mean field kinetic model for systems of rational agents interacting in a game theoretical framework. This model is inspired from non-cooperative anonymous games with a continuum of players and Mean-Field Games. The large time behavior of the system is given by a macroscopic closure with a Nash equilibrium serving as the local thermodynamic equilibrium. Applications of the presented theory to social and economical models will be given. We propose a mean field kinetic model for systems of rational agents interacting in a game theoretical framework. This model is inspired from non-cooperative anonymous games with a continuum of players and Mean-Field Games. The large time behavior of the system is given by a macroscopic closure with a Nash equilibrium serving as the local thermodynamic equilibrium. Applications of the presented theory to social and economical models will be ...

91B80 ; 35Q82 ; 35Q91

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Research talks

Mean field games (MFG) are dynamic games with infinitely many infinitesimal agents. In this joint work with Catherine Rainer (U. Brest), we study the efficiency of Nash MFG equilibria: Namely, we compare the social cost of a MFG equilibrium with the minimal cost a global planner can achieve. We find a structure condition on the game under which there exists efficient MFG equilibria and, in case this condition is not fulfilled, quantify how inefficient MFG equilibria are. Mean field games (MFG) are dynamic games with infinitely many infinitesimal agents. In this joint work with Catherine Rainer (U. Brest), we study the efficiency of Nash MFG equilibria: Namely, we compare the social cost of a MFG equilibrium with the minimal cost a global planner can achieve. We find a structure condition on the game under which there exists efficient MFG equilibria and, in case this condition is not fulfilled, quantify how ...

91A13 ; 35Q91

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Research talks

In the talk, I will first present a typical Mean Field Game problem, as in the theory introduced by Lasry-Lions and Huang-Caines-Malhamé, concentrating on the case where the game has a variational structure (i.e., the equilibrium can be found by minimizing a global energy) and is purely deterministic (no diffusion, no stochastic control). From the game-theoretical point of view, we look for a Nash equilibrium for a non-atomic congestion game, involving a penalization on the density of the players at each point. I will explain why regularity questions are natural and useful for rigorously proving that minimizers are equilibria, making the connection with what has been done for the incompressible Euler equation in the Brenier’s variational formalism. I will also introduce a variant where the penalization on the density is replaced by a constraint, which lets a price (which is a pressure, in the incompressible fluid language) appears on saturated regions. Then, I will sketch some regularity results which apply to these settings.
The content of the talk mainly comes from joint works with A. Mészáros, P. Cardaliaguet, and H. Lavenant.
In the talk, I will first present a typical Mean Field Game problem, as in the theory introduced by Lasry-Lions and Huang-Caines-Malhamé, concentrating on the case where the game has a variational structure (i.e., the equilibrium can be found by minimizing a global energy) and is purely deterministic (no diffusion, no stochastic control). From the game-theoretical point of view, we look for a Nash equilibrium for a non-atomic congestion game, ...

49J45 ; 91A10 ; 35Q91

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- x; 221 p.
ISBN 978-0-8218-8794-3

Graduate studies in mathematics , 0136

Localisation : Collection 1er étage;Réserve

problème aux valeurs limites # problème de limite libre # régularité optimale

35R35 ; 35-02 ; 35Q91 ; 35B65

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