Calculus of Variations and Geometric Measure Theory

J. D. Benamou - G. Carlier - F. Santambrogio

Variational Mean Field Games

created by santambro on 30 Mar 2016
modified on 20 Jul 2016


Accepted Paper

Inserted: 30 mar 2016
Last Updated: 20 jul 2016

Journal: "Active Particles, Volume 1: Theory, Models, Applications"
Year: 2016


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.