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 language | English (US) |
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Pages (from-to) | 613-639 |
Number of pages | 27 |
Journal | Theory of Probability and its Applications |
Volume | 66 |
Issue number | 4 |
DOIs | |
State | Published - 2022 |
Keywords
- Nash equilibrium
- exterior noise
- mean field game
- stochastic control
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty