Stochastic Differential Mean-Field Games in a Weak Formulation

2023/09/09 by Morgado, Hector Sanchez, Sierra, Jesus
#35Q89 #49N80 #91A15 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2309.04647

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.

Related

• Mean Field Forward-Backward Stochastic Differential Equations
• Strong solutions to submodular mean field games with common noise and related McKean-Vlasov FBSDEs
• Controlled diffusion Mean Field Games with common noise, and McKean-Vlasov second order backward SDEs
• Mean field games with common noise and degenerate idiosyncratic noise
• Strong solutions of mean-field FBSDEs and their applications to multi-population mean-field games