Well-posedness of fully coupled Mckean–Vlasov FBSDE and application to Stackelberg games

School of Mathematics, Shandong University, Jinan 250100, PR China.

^* Corresponding author: nietianyang@sdu.edu.cn

Received: 8 September 2024
Accepted: 24 April 2025

Abstract

In this paper, motivated by the study of linear-quadratic (LQ) Stackelberg differential games of McKean–Vlasov type, we investigate the solvability for the McKean–Vlasov forward–backward stochastic differential equations (MV-FBSDEs). Inspired by the work of Tian and Yu (2023), we propose a type of domination-monotonicity conditions. Under these conditions and Lipschitz condition, we prove the well-posedness of such MV-FBSDEs by the method of continuation. As an application, we consider the LQ Stackelberg differential games of McKean–Vlasov type. The related Stackelberg solutions are given explicitly by the solutions of MV-FBSDEs. The feedback form of Stackelberg solutions is also given through Riccati equations. In some special but nontrivial cases, we prove the solvability of these Riccati equations by linear transformation.