Seminar Date: 2021-01-07
In this talk we give an introduction to Mean Field Games, introduced by Lasry-Lions and Huang-Caines-Malhamé in 2006-07, which models a game with a number of atomic players tending to infinity. The limit behavior collapses in a coupled system of PDE’s: a Fokker-Plank equation and a Hamilton-Jacobi-Bellman equation. A particular discretization of the system of coupled PDEs can be seen as the first order optimality condition of a finite-dimensional non-smooth convex optimization problem, which can be solved by several proximal splitting methods in the literature. We provide a review on proximal splitting algorithms, we apply them in our context, and we provide numerical comparisons including several methods available in the literature. Joint work with F. Silva and D. Kalise.