François Delarue - Mean Field Games

I will make a presentation of the theory of mean field games, introduced 15 years ago by two groups of researchers, Lasry and Lions in France, and Caines, Huang and Malhamé in Canada. This is a theory for games with many agents with weak interaction. The very purpose of it is to address directly the limiting game with an infinite number of agents. The theory has drawn of lot of attention in mathematics as it uses tools from different areas (PDE, probability, calculs of variations). The first part of my talk will be dedicated to the roots of the theory. In a second part, I will focus on more recent objects, like the master equation, which is a PDE set on the space of probability measures and which is the analogue of the so-called Nash system in game theory but in infinite dimension. I will review some of the recent works in this direction and some questions that are left open. King's Mathematical Colloquium on December 15th, 2022