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Variational Mean Field Games

Benamou, Jean-David; Carlier, Guillaume; Santambrogio, Filippo (2017), Variational Mean Field Games, in Nicola Bellomo, Pierre Degond, Eitan Tadmor, Active Particles, Volume 1, Springer : Berlin Heidelberg, p. 141-171. 10.1007/978-3-319-49996-3_4

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Type
Chapitre d'ouvrage
Date
2017
Book title
Active Particles, Volume 1
Book author
Nicola Bellomo, Pierre Degond, Eitan Tadmor
Publisher
Springer
Published in
Berlin Heidelberg
ISBN
978-3-319-49994-9
Pages
141-171
Publication identifier
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Author(s)
Benamou, Jean-David
Carlier, Guillaume
Santambrogio, Filippo
Abstract (EN)
This paper is a brief presentation of those Mean Field Games with congestion penalization which have a variational structure, starting from the deterministic dynamical framework. The stochastic framework (i.e. with diffusion) is also presented both in the stationary and dynamic case. The variational problems relevant for MFG are described via Eulerian and Lagrangian languages, and the connection with equilibria is explained by means of convex duality and of optimality conditions. The convex structure of the problem also allows for efficient numerical treatment, based on Augmented Lagrangian Algorithms, and some new simulations are shown at the end of the paper.
Subjects / Keywords
Mean Field Games