Probabilistic Approach to Mean Field Games
In this talk, we examine numerical methods for solving forward backward stochastic differential equations (FBSDEs) of McKean-Vlasov type. We are particularly interested in equations of this type as they represent the solutions to mean field games from the probabilistic viewpoint.
Mean field games were developed independently and at about the same time by Lasry and Lions, and Huang, Caines, and Malhame. The goal of mean field games is to understand the limit as $N \rightarrow \infty$ for an N-player stochastic game. They can be used to analyze dynamics with a large number of symmetric players which each have a small effect on the dynamics of the group. The applications of mean field games are numerous, and spread across many disciplines, including social science (congestion, cyber security), biology (flocking, swarming, circadian rhythms), and economics (stock prices, production of exhaustible resources, bank run), just to name a few.