title: Schrödinger Approach to Mean Field Games.
abstract: Mean field games (MFG) provide a theoretical frame to model socioeconomic systems. In this Letter, we study a particular class of MFG that shows strong analogies with the nonlinear Schrödinger and Gross-Pitaevskii equations introduced in physics to describe a variety of physical phenomena. Using this bridge, many results and techniques developed along the years in the latter context can be transferred to the former, which provides both a new domain of application for the nonlinear Schrödinger equation and a new and fruitful approach in the study of mean field games. Utilizing this approach, we analyze in detail a population dynamics model in which the "players" are under a strong incentive to coordinate themselves.
authors.affiliation: LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France.|LPTM, CNRS, Université Cergy-Pontoise, 95302 Cergy-Pontoise, France.
authors.forename: Igor
authors.initials: I
authors.lastname: Swiecicki
authors.affiliation: LPTM, CNRS, Université Cergy-Pontoise, 95302 Cergy-Pontoise, France.
authors.forename: Thierry
authors.initials: T
authors.lastname: Gobron
authors.affiliation: LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France.
authors.forename: Denis
authors.initials: D
authors.lastname: Ullmo