On the Regularity of a Weak Formulation of Stochastic Differential Mean-Field Games

We study a McKean-Vlasov Forward-Backward Stochastic Differential Equation (FBSDE) in connection with the theory of Stochastic Differential Mean-Field games, particularly the weak (non-fully coupled) formulation described in Section 3.3.1 of the book “Probabilistic theory of mean field games with applications” by Carmona and Delarue. Our main goal is to obtain regularity results for this McKean-Vlasov FBSDE, specifically classical and Malliavin differentiability