Universal behavior in non stationary Mean Field Games – Archive ouverte HAL

Thibault Bonnemain ¹ Thierry Gobron ² Denis Ullmo ¹

Thibault Bonnemain, Thierry Gobron, Denis Ullmo. Universal behavior in non stationary Mean Field Games. Physics Letters A, Elsevier, 2020, ⟨10.1016/j.physleta.2020.126608⟩. ⟨hal-02361330⟩

Mean Field Games provide a powerful framework to analyze the dynamics of a large number of controlled objects in interaction. Though these models are much simpler than the underlying differential games they describe in some limit, their behavior is still far from being fully understood. When the system is confined, a notion of « ergodic state » has been introduced that characterizes most of the dynamics for long optimization times. Here we consider a class of models without such an ergodic state, and show the existence of a scaling solution that plays similar role. Its universality and scaling behavior can be inferred from a mapping to an electrostatic problem.

• 1. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
• 2. LPTM – UMR 8089 – Laboratoire de Physique Théorique et Modélisation