Direct approach of linear-quadratic Stackelberg mean field games of backward-forward stochastic systems

• Published in: Chinese Control Conference pp. 1230 - 1237
• Main Authors: Cong, Wenyu, Shi, Jingtao
• Format: Conference Proceeding
• Language: English
• Published: Technical Committee on Control Theory, Chinese Association of Automation 28.07.2024
• Subjects: Costs; Differential equations; Differential games; direct approach; FBSDE; Games; LQ stochastic optimal control; Noise; Optimal control; Stackelberg equilibrium; Stackelberg mean field game; Stochastic systems
• ISSN: 1934-1768
• DOI: 10.23919/CCC63176.2024.10662561

This paper is concerned with a linear-quadratic (LQ) Stackelberg mean field games of backward-forward stochastic systems, involving a backward leader and a substantial number of forward followers. The leader initiates by providing its strategy, and subsequently, each follower optimizes its individual cost. A direct approach is applied to solve this game. Initially, we address a mean field game problem, determining the optimal response of followers to the leader's strategy. Following the implementation of followers' strategies, the leader faces an optimal control problem driven by high-dimensional forward-backward stochastic differential equations (FBSDEs). Through the decoupling of the high-dimensional Hamiltonian system using mean field approximations, we formulate a set of decentralized strategies for all players, demonstrated to be an \left(\epsilon_{1}, \epsilon_{2}\right) Stackelberg equilibrium.