Mean field games

Friday September 14th, 14h-16h30

Slides

Olivier Guéant (Paris 1), An introduction to mean field games and their applications.

Abstract

The goal of this 2-hour talk is to present mean field game theory (introduced by Lasry and Lions) and its applicability to a wide variety of situations/problems. The theory of (stochastic) optimal control will be recalled along with the associated partial differential equations. The need for mean field games will then be justified by optimal control problems faced by multiple agents in interactions with one another. The main equations and the main results of the theory will be presented. Applications and numerical recipes will be discussed. Mean field games in discrete structures, such as graphs, will also be discussed in depth.

Papers

  • Lasry, J. M., & Lions, P. L. (2007). Mean field games. Japanese journal of mathematics, 2(1), 229-260.
  • Guéant, O., Lasry, J. M., & Lions, P. L. (2011). Mean field games and applications. In Paris-Princeton lectures on mathematical finance 2010 (pp. 205-266). Springer, Berlin, Heidelberg.
  • Guéant, O. (2015). Existence and uniqueness result for mean field games with congestion effect on graphs. Applied Mathematics & Optimization, 72(2), 291-303.
  • Achdou, Y., & Capuzzo-Dolcetta, I. (2010). Mean field games: numerical methods. SIAM Journal on Numerical Analysis, 48(3), 1136-1162.

Resources