English

Controlled diffusion Mean Field Games with common noise, and McKean-Vlasov second order backward SDEs

Probability 2020-05-18 v1 Optimization and Control

Abstract

We consider a mean field game with common noise in which the diffusion coefficients may be controlled. We prove existence of a weak relaxed solution under some continuity conditions on the coefficients. We then show that, when there is no common noise, the solution of this mean field game is characterized by a McKean-Vlasov type second order backward SDE.

Keywords

Cite

@article{arxiv.2005.07542,
  title  = {Controlled diffusion Mean Field Games with common noise, and McKean-Vlasov second order backward SDEs},
  author = {Adrien Barrasso and Nizar Touzi},
  journal= {arXiv preprint arXiv:2005.07542},
  year   = {2020}
}