English

A quadratic Mean Field Games model for the Langevin equation

Analysis of PDEs 2021-01-12 v3 Optimization and Control

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 [9], 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.

Keywords

Cite

@article{arxiv.2007.10620,
  title  = {A quadratic Mean Field Games model for the Langevin equation},
  author = {Fabio Camilli},
  journal= {arXiv preprint arXiv:2007.10620},
  year   = {2021}
}