Mean Field Games (MFGs) have been introduced independently by Lasry-Lions and Huang, Malhamé and Caines in 2006. The main purpose of this theory is to simplify the analysis of stochastic differential games with a large number of small and indistinguishable players. Applications of MFGs include models in Economics, Mathematical Finance, Social Sciences and Engineering. In its simplest form, an equilibrium in MFG theory is characterized by a system of PDEs consisting of a Hamilton-Jacobi-Bellman equation and a Fokker-Planck-Kolmogorov equation. In some particular cases, this PDE system corresponds, at least formally, to the first order optimality condition of an associated variational problem. This class of MFGs is called “variational MFGs”. In this talk we will review some theoretical and numerical techniques for variational MFGs that allow us to characterize and compute the associated Nash equilibria.

(Zoom meeting: Link – pass: 1234)