Lagrangian discretization of variational mean field games - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

Lagrangian discretization of variational mean field games

Clément Sarrazin

Résumé

In this article, we introduce a method to approximate solutions of some variational mean field game problems with congestion, by finite sets of player trajectories. These trajectories are obtained by solving a minimization problem, similar to the initial variational problem. In this discretized problem, congestion is penalized by a Moreau envelop with the 2-Wasserstein distance. Study of this envelop as well as efficient computation of its values and variations is done using semi-discrete optimal transport. We show convergence of the discrete sets of trajectories toward a solution of the mean field game, as well as conditions on the discretization in order to get this convergence. We also show strong convergence (in particular almost everywhere) in some cases for the underlying densities resulting from the Moreau projection of solution to the discrete problem.
Fichier principal
Vignette du fichier
main.pdf (2.49 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02951808 , version 1 (22-10-2020)

Identifiants

  • HAL Id : hal-02951808 , version 1

Citer

Clément Sarrazin. Lagrangian discretization of variational mean field games. 2020. ⟨hal-02951808⟩
57 Consultations
45 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More