LAGRANGIAN DISCRETIZATION OF VARIATIONAL MEAN FIELD GAMES.
- Resource Type
- Article
- Authors
- SARRAZIN, CLÉMENT
- Source
- SIAM Journal on Control & Optimization. 2022, Vol. 60 Issue 3, p1365-1392. 28p.
- Subject
- *GAMES
*PROBLEM solving
- Language
- ISSN
- 0363-0129
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 envelope with 2-Wasserstein distance. Study of this envelope 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. [ABSTRACT FROM AUTHOR]