Backward Linear-Quadratic Mean Field Stochastic Differential Games: A Direct Method
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917850935984128 |
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| author | Si, Yu Shi, Jingtao |
| author_facet | Si, Yu Shi, Jingtao |
| contents | This paper studies a linear-quadratic mean-field game of stochastic large-population system, where the large-population system satisfies a class of $N$ weakly coupled linear backward stochastic differential equation. Different from the fixed-point approach commonly used to address large population problems, we first directly apply the maximum principle and decoupling techniques to solve a multi-agent problem, obtaining a centralized optimal strategy. Then, by letting $N$ tend to infinity, we establish a decentralized optimal strategy. Subsequently, we prove that the decentralized optimal strategy constitutes an $ε$-Nash equilibrium for this game. Finally, we provide a numerical example to simulate our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18891 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Backward Linear-Quadratic Mean Field Stochastic Differential Games: A Direct Method Si, Yu Shi, Jingtao Optimization and Control 93E20, 60H10, 49K45, 49N80, 91A23 This paper studies a linear-quadratic mean-field game of stochastic large-population system, where the large-population system satisfies a class of $N$ weakly coupled linear backward stochastic differential equation. Different from the fixed-point approach commonly used to address large population problems, we first directly apply the maximum principle and decoupling techniques to solve a multi-agent problem, obtaining a centralized optimal strategy. Then, by letting $N$ tend to infinity, we establish a decentralized optimal strategy. Subsequently, we prove that the decentralized optimal strategy constitutes an $ε$-Nash equilibrium for this game. Finally, we provide a numerical example to simulate our results. |
| title | Backward Linear-Quadratic Mean Field Stochastic Differential Games: A Direct Method |
| topic | Optimization and Control 93E20, 60H10, 49K45, 49N80, 91A23 |
| url | https://arxiv.org/abs/2411.18891 |