Schrödinger approach to Mean Field Games with negative coordination – Archive ouverte HAL

Thibault Bonnemain ¹ Thierry Gobron ² Denis Ullmo ¹

Thibault Bonnemain, Thierry Gobron, Denis Ullmo. Schrödinger approach to Mean Field Games with negative coordination. SciPost Physics, SciPost Foundation, 2020, ⟨10.21468/SciPostPhys.9.4.059⟩. ⟨hal-02923105⟩

Mean Field Games provide a powerful framework to analyze the dynamics of a large number of controlled agents in interaction. Here we consider such systems when the interactions between agents result in a negative coordination and analyze the behavior of the associated system of coupled PDEs using the now well established correspondence with the non linear Schr\ »odinger equation. We focus on the long optimization time limit and on configurations such that the game we consider goes through different regimes in which the relative importance of disorder, interactions between agents and external potential varies, which makes possible to get insights on the role of the forward-backward structure of the Mean Field Game equations in relation with the way these various regimes are connected.

• 1. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
• 2. LPP – Laboratoire Paul Painlevé – UMR 8524