Direct Approach of Indefinite Linear-Quadratic Mean Field Games
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909232775823360 |
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| author | Cong, Wenyu Shi, Jingtao |
| author_facet | Cong, Wenyu Shi, Jingtao |
| contents | This paper is concerned with an indefinite linear-quadratic mean field games of stochastic large-population system, where the individual diffusion coefficients can depend on both the state and the control of the agents. Moreover, the control weights in the cost functionals could be indefinite. A direct approach is used to derive the $ε$-Nash equilibrium strategy. First, we formally solving an $N$-player game problem within a vast and finite population setting. Subsequently, decoupling or reducing high-dimensional systems by introducing two Riccati equations explicitly yields centralized strategies, contingent on the state of a specific player and the average state of the population. As the population size $N$ goes infinity, the construction of decentralized strategies becomes feasible. Then, we demonstrated they are an $ε$-Nash equilibrium. Numerical examples are provided to demonstrate the effectiveness of the proposed strategies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05166 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Direct Approach of Indefinite Linear-Quadratic Mean Field Games Cong, Wenyu Shi, Jingtao Optimization and Control 93E20, 60H10, 49K45, 49N70, 91A23 This paper is concerned with an indefinite linear-quadratic mean field games of stochastic large-population system, where the individual diffusion coefficients can depend on both the state and the control of the agents. Moreover, the control weights in the cost functionals could be indefinite. A direct approach is used to derive the $ε$-Nash equilibrium strategy. First, we formally solving an $N$-player game problem within a vast and finite population setting. Subsequently, decoupling or reducing high-dimensional systems by introducing two Riccati equations explicitly yields centralized strategies, contingent on the state of a specific player and the average state of the population. As the population size $N$ goes infinity, the construction of decentralized strategies becomes feasible. Then, we demonstrated they are an $ε$-Nash equilibrium. Numerical examples are provided to demonstrate the effectiveness of the proposed strategies. |
| title | Direct Approach of Indefinite Linear-Quadratic Mean Field Games |
| topic | Optimization and Control 93E20, 60H10, 49K45, 49N70, 91A23 |
| url | https://arxiv.org/abs/2404.05166 |