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

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 individua...

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Bibliographic Details
Published inChinese Control Conference pp. 1230 - 1237
Main Authors Cong, Wenyu, Shi, Jingtao
Format Conference Proceeding
LanguageEnglish
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
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Summary: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.
ISSN:1934-1768
DOI:10.23919/CCC63176.2024.10662561