Direct Approach of Linear-Quadratic Stackelberg Mean Field Games of Backward-Forward Stochastic Systems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910503442317312 |
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| author | Cong, Wenyu Shi, Jingtao |
| author_facet | Cong, Wenyu Shi, Jingtao |
| contents | 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 $(ε_1, ε_2)$-Stackelberg equilibrium. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15835 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Direct Approach of Linear-Quadratic Stackelberg Mean Field Games of Backward-Forward Stochastic Systems Cong, Wenyu Shi, Jingtao Optimization and Control 93E20, 60H10, 49K45, 49N70, 91A23 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 $(ε_1, ε_2)$-Stackelberg equilibrium. |
| title | Direct Approach of Linear-Quadratic Stackelberg Mean Field Games of Backward-Forward Stochastic Systems |
| topic | Optimization and Control 93E20, 60H10, 49K45, 49N70, 91A23 |
| url | https://arxiv.org/abs/2401.15835 |