Working Paper Article Version 1 This version is not peer-reviewed

A Quadratic Mean Field Games Model for the Langevin Equation

Version 1 : Received: 10 January 2021 / Approved: 12 January 2021 / Online: 12 January 2021 (09:31:54 CET)

How to cite: Camilli, F. A Quadratic Mean Field Games Model for the Langevin Equation. Preprints 2021, 2021010211 Camilli, F. A Quadratic Mean Field Games Model for the Langevin Equation. Preprints 2021, 2021010211

Abstract

We consider a Mean Field Games model where the dynamics of the agents is given by a controlled Langevin equation and the cost is quadratic. A change of variables, introduced in [13], transforms the Mean Field Games system into a system of two coupled kinetic Fokker-Planck equations. We prove an existence result for the latter system, obtaining consequently existence of a solution for the Mean Field Games system.

Subject Areas

Langevin equation; Mean Field Games system; kinetic Fokker-Planck equation

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