Linear-Quadratic Partially Observed Mean Field Stackelberg Stochastic Differential Game with Applications
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918234924515328 |
|---|---|
| author | Si, Yu Zheng, Yueyang Shi, Jingtao |
| author_facet | Si, Yu Zheng, Yueyang Shi, Jingtao |
| contents | This paper is concerned with a linear-quadratic partially observed mean field Stackelberg stochastic differential game, which contains a leader and a large number of followers. Specifically, the followers confront a large-population Nash game subsequent to the leader's initial announcement of his strategy. In turn, the leader optimizes his own cost functional, taking into account the anticipated reactions of the followers. The state equations of both the leader and the followers are general stochastic differential equations, where the drift terms contain both the state average term and the state expectation term. However, the followers' state average terms enter into the drift term of the leader's state equation and the state expectation term of the leader enters into the state equation of the follower, reflecting the mutual influence between the leader and the followers. By utilizing the techniques of state decomposition and backward separation principle, we deduce the open-loop adapted decentralized strategies and feedback decentralized strategies of this leader-followers system, and demonstrate that the decentralized strategies are the corresponding $\varepsilon$-Stackelberg-Nash equilibrium. Finally, we apply the theoretical result to a product planning problem with sticky prices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15803 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear-Quadratic Partially Observed Mean Field Stackelberg Stochastic Differential Game with Applications Si, Yu Zheng, Yueyang Shi, Jingtao Optimization and Control 93E20, 60H10, 49K45, 49N70, 91A23 This paper is concerned with a linear-quadratic partially observed mean field Stackelberg stochastic differential game, which contains a leader and a large number of followers. Specifically, the followers confront a large-population Nash game subsequent to the leader's initial announcement of his strategy. In turn, the leader optimizes his own cost functional, taking into account the anticipated reactions of the followers. The state equations of both the leader and the followers are general stochastic differential equations, where the drift terms contain both the state average term and the state expectation term. However, the followers' state average terms enter into the drift term of the leader's state equation and the state expectation term of the leader enters into the state equation of the follower, reflecting the mutual influence between the leader and the followers. By utilizing the techniques of state decomposition and backward separation principle, we deduce the open-loop adapted decentralized strategies and feedback decentralized strategies of this leader-followers system, and demonstrate that the decentralized strategies are the corresponding $\varepsilon$-Stackelberg-Nash equilibrium. Finally, we apply the theoretical result to a product planning problem with sticky prices. |
| title | Linear-Quadratic Partially Observed Mean Field Stackelberg Stochastic Differential Game with Applications |
| topic | Optimization and Control 93E20, 60H10, 49K45, 49N70, 91A23 |
| url | https://arxiv.org/abs/2503.15803 |