{"ID":2887205,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.01568","arxiv_id":"2508.01568","title":"Indefinite Linear-Quadratic Partially Observed Mean-Field Game","abstract":"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.","short_abstract":"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 rathe...","url_abs":"https://arxiv.org/abs/2508.01568","url_pdf":"https://arxiv.org/pdf/2508.01568v1","authors":"[\"Tian Chen\",\"Tianyang Nie\",\"Zhen Wu\"]","published":"2025-08-03T03:36:37Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}