Decentralized Strategies for Backward Linear-Quadratic Mean Field Games and Teams
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916558159216640 |
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| author | Si, Yu Shi, Jingtao |
| author_facet | Si, Yu Shi, Jingtao |
| contents | This paper studies a new class of linear-quadratic mean field games and teams problem, where the large-population system satisfies a class of $N$ weakly coupled linear backward stochastic differential equations (BSDEs), and $z_i$ (a part of solution of BSDE) enter the state equations and cost functionals. By virtue of stochastic maximum principle and optimal filter technique, we obtain a Hamiltonian system first, which is a fully coupled forward-backward stochastic differential equation (FBSDE). Decoupling the Hamiltonian system, we derive a feedback form optimal strategy by introducing Riccati equations, stochastic differential equation (SDE) and BSDE. Finally, we provide a numerical example to simulate our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decentralized Strategies for Backward Linear-Quadratic Mean Field Games and Teams Si, Yu Shi, Jingtao Optimization and Control 93E20, 60H10, 49K45, 49N70, 91A23 This paper studies a new class of linear-quadratic mean field games and teams problem, where the large-population system satisfies a class of $N$ weakly coupled linear backward stochastic differential equations (BSDEs), and $z_i$ (a part of solution of BSDE) enter the state equations and cost functionals. By virtue of stochastic maximum principle and optimal filter technique, we obtain a Hamiltonian system first, which is a fully coupled forward-backward stochastic differential equation (FBSDE). Decoupling the Hamiltonian system, we derive a feedback form optimal strategy by introducing Riccati equations, stochastic differential equation (SDE) and BSDE. Finally, we provide a numerical example to simulate our results. |
| title | Decentralized Strategies for Backward Linear-Quadratic Mean Field Games and Teams |
| topic | Optimization and Control 93E20, 60H10, 49K45, 49N70, 91A23 |
| url | https://arxiv.org/abs/2501.04717 |