Non-linear Schrödinger approach to mean field games
Denis Ullmo (LPTMS, Université Paris-Sud)
Mean field games theory is a rather recent research area, at the frontier between applied mathematics, social sciences and physics. It was initiated a decade ago by Pierre-Louis Lions and Jean-Michel Lasry as a tool to model certain social phenomena involving a significant number of actors – through a game theory approach – while maintaining a reasonable level of simplicity thanks to the concept of mean-field imported from physics.
In this presentation, after a general introduction to Mean Field Games, I will show that there is a formal, but deep, link between an important class of these models and the nonlinear Schrödinger equation familiar to physicists. This link makes it possible to develop a deeper understanding of the behavior of Mean Field Games. A specific example will be treated in details and will demonstrate how various concepts developed by physicist while studying the non-linear Schrödinger equation can be used with profit in the context of Mean Field Games.
- Igor Swiecicki, Thierry Gobron, and Denis Ullmo, Schrödinger Approach to Mean Field Games, Phys. Rev. Lett. 116, 128701 (2016).