Rene Carmona

Rene Carmona, Princeton University

Mean Field Games: theory and applications

We review the Mean Field Game paradigm introduced independently by Caines-Huang-Malhame and Lasry-Lyons ten years ago, and we illustrate their relevance to applications with a couple of examples (bird flocking and room exit). We then review the probabilistic approach based on Forward-Backward Stochastic Differential Equations, and we derive the Master Equation  from a version of the chain rule (Ito's formula) for functions over flows of probability measures. Finally, motivated by the literature on economic models of bank runs, we introduce mean field games of timing and discuss new results, and some of the many remaining challenges.