CONTROLLED DIFFUSION MEAN FIELD GAMES WITH COMMON NOISE AND MCKEAN–VLASOV SECOND ORDER BACKWARD SDEs

A. Barrasso, N. Touzi

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)613-639
Number of pages27
JournalTheory of Probability and its Applications
Volume66
Issue number4
DOIs
StatePublished - 2022

Keywords

  • Nash equilibrium
  • exterior noise
  • mean field game
  • stochastic control

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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