Stochastic Differential Mean-Field Games in a Weak Formulation

Abstract: We study a Mean Field Game system in a weak formulation through its associated McKean-Vlasov Forward-Backward Stochastic Differential Equation (FBSDE). Our main goal is to obtain existence and regularity results of this FBSDE using the techniques of Malliavin calculus, in particular, classical and Malliavin differentiability. Using these results, we characterize the decoupling (master) field.