Finite Difference Schemes for Mean Field Games

Monday, November 12, 2012 - 3:10pm - 4:10pm
Keller 3-180
Yves Achdou (Université de Paris VII (Denis Diderot))
Mean field type models describing the limiting behavior of stochastic differential game problems as the number of players tends to infinity, have been recently introduced by J-M. Lasry and P-L. Lions.

They may lead to systems of evolutive partial differential equations coupling a forward Bellman equation and a backward Fokker-Planck equation. The forward-backward structure is an important feature of this system, which makes it necessary to design new strategies for mathematical analysis and
numerical approximation.

In this survey, several aspects of a finite difference method used to approximate the previously mentioned system of PDEs are discussed, including:
existence and uniqueness properties, a priori bounds on the solutions of the discrete schemes, convergence, and algorithms for solving the resulting
nonlinear systems of equations. Some numerical experiments are presented.

Collaborators: F. Camilli, I. Capuzzo Dolcetta, V. Perez