# Séminaire du LPTMS: Denis Ullmo

## 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.

Reference:

- Igor Swiecicki, Thierry Gobron, and Denis Ullmo,
*Schrödinger Approach to Mean Field Games*, Phys. Rev. Lett.**116**, 128701 (2016).

**Date/Time : ** 07/03/2017 - *11:00 - 12:00*

**Location : ** LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay

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