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Séminaires, soutenances
Schrödinger Approach to Mean Field Games
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Europe/Paris
Amphi Recherche
Amphi Recherche
Description
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 game, I will show that there is a formal, but deep, link between an important class of these models and the nonlinear Schrödinger (or Gross-Pitaevskii) equation encountered in many circumstances in physics, and which describes in particular the evolution of a set of interacting bosons. This link makes it possible to develop highly effective approximation schemes to solve the mean field game equations. I would show in particular how to obtain in this way an understanding both detailed and intuitive of a population dynamics model wherein the agents are under a strong incentive to coordinate themselves.
