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arXiv · 2508.01568

Indefinite Linear-Quadratic Partially Observed Mean-Field Game

Tian Chen·Tianyang Nie·Zhen Wu
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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.

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Tian Chen, Tianyang Nie, Zhen Wu. 2025-08-03. Indefinite Linear-Quadratic Partially Observed Mean-Field Game. https://arxiv.org/abs/2508.01568

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