Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Variational Mean Field Games

Abstract : 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.
Complete list of metadatas

Cited literature [30 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01295299
Contributor : Filippo Santambrogio <>
Submitted on : Friday, April 15, 2016 - 1:20:55 AM
Last modification on : Wednesday, February 19, 2020 - 8:53:07 AM
Document(s) archivé(s) le : Monday, November 14, 2016 - 9:21:41 AM

File

BenCarSan-v4.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01295299, version 1

Citation

Jean-David Benamou, Guillaume Carlier, Filippo Santambrogio. Variational Mean Field Games. 2016. ⟨hal-01295299⟩

Share

Metrics

Record views

994

Files downloads

633