Quadratic Mean Field Games - Archive ouverte HAL Access content directly
Journal Articles Physics Reports Year : 2019

Quadratic Mean Field Games

Abstract

Mean field games were introduced independently by J-M. Lasry and P-L. Lions, and by M. Huang, R.P. Malham\'e and P. E. Caines, in order to bring a new approach to optimization problems with a large number of interacting agents. The description of such models split in two parts, one describing the evolution of the density of players in some parameter space, the other the value of a cost functional each player tries to minimize for himself, anticipating on the rational behavior of the others. Quadratic Mean Field Games form a particular class among these systems, in which the dynamics of each player is governed by a controlled Langevin equation with an associated cost functional quadratic in the control parameter. In such cases, there exists a deep relationship with the non-linear Schr\"odinger equation in imaginary time, connexion which lead to effective approximation schemes as well as a better understanding of the behavior of Mean Field Games. The aim of this paper is to serve as an introduction to Quadratic Mean Field Games and their connexion with the non-linear Schr\"odinger equation, providing to physicists a good entry point into this new and exciting field.
Fichier principal
Vignette du fichier
S0370157319300018.pdf (1.01 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-02291869 , version 1 (22-10-2021)

Licence

Identifiers

Cite

Denis Ullmo, Igor Swiecicki, Thierry Gobron. Quadratic Mean Field Games. Physics Reports, 2019, ⟨10.1016/j.physrep.2019.01.001⟩. ⟨hal-02291869⟩
39 View
65 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More