Indefinite Linear-Quadratic Partially Observed Mean-Field Game
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915423390269440 |
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| author | Chen, Tian Nie, Tianyang Wu, Zhen |
| author_facet | Chen, Tian Nie, Tianyang Wu, Zhen |
| contents | This paper investigates an indefinite linear-quadratic partially observed mean-field game with common noise, incorporating both state-average and control-average effects. In our model, each agent's state is observed through both individual and public observations, which are modeled as general stochastic processes rather than Brownian motions. {It is noteworthy that} the weighting matrices in the cost functional are allowed to be indefinite. We derive the optimal decentralized strategies using the Hamiltonian approach and establish the well-posedness of the resulting Hamiltonian system by employing a relaxed compensator. The associated consistency condition and the feedback representation of decentralized strategies are also established. Furthermore, we demonstrate that the set of decentralized strategies form an $\varepsilon$-Nash equilibrium. As an application, we solve a mean-variance portfolio selection problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_01568 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Indefinite Linear-Quadratic Partially Observed Mean-Field Game Chen, Tian Nie, Tianyang Wu, Zhen Optimization and Control 91A16, 49N10, 91A10, 93C41 This paper investigates an indefinite linear-quadratic partially observed mean-field game with common noise, incorporating both state-average and control-average effects. In our model, each agent's state is observed through both individual and public observations, which are modeled as general stochastic processes rather than Brownian motions. {It is noteworthy that} the weighting matrices in the cost functional are allowed to be indefinite. We derive the optimal decentralized strategies using the Hamiltonian approach and establish the well-posedness of the resulting Hamiltonian system by employing a relaxed compensator. The associated consistency condition and the feedback representation of decentralized strategies are also established. Furthermore, we demonstrate that the set of decentralized strategies form an $\varepsilon$-Nash equilibrium. As an application, we solve a mean-variance portfolio selection problem. |
| title | Indefinite Linear-Quadratic Partially Observed Mean-Field Game |
| topic | Optimization and Control 91A16, 49N10, 91A10, 93C41 |
| url | https://arxiv.org/abs/2508.01568 |