TBA

I will make a presentation on 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 a lot of attention in mathematics as it uses tools from different areas (PDE, probability, calculus of variations). The first part of my talk will be dedicated to the roots of the theory. In the 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 analog of the so-called Nash system in game theory but in an infinite dimension. I will review some of the recent works in this direction and some questions that are left open.