The first part of this talk will review the early developments in the mathematical theory that began with the introduction of Mean Field Games twenty years ago. We will briefly discuss several applications to highlight the need for an asymptotic analysis in the search for Nash equilibria and social optima in competitive and cooperative large populations. Additionally, we will explain why and how a probabilistic approach was introduced to complement and enhance the original partial differential equation approach to these problems. Next, we will introduce the concept of the master equation and its role in renewing interest in optimal transportation and the analysis of partial differential equations in the Wasserstein space of probability measures. Finally we will discuss some of the new challenges currently investigated.

Reception to follow in the Mathematics Common Room.