This paper considers a class of linear-quadratic-Gaussian (LQG) mean-field games (MFGs) with partial observation structure for individual agents. Unlike other literature, there are some special features in our formulation. First, the individual state is driven by some common-noise due to the external factor and the state-average thus becomes a random process instead of a deterministic quantity. Second, the sensor function of individual observation depends on state-average thus the agents are coupled in triple manner: not only in their states and cost functionals, but also through their observation mechanism. The decentralized strategies for individual agents are derived by the Kalman filtering and separation principle. The consistency condition is obtained which is equivalent to the wellposedness of some forward-backward stochastic differential equation (FBSDE) driven by common noise. Finally, the related $ \epsilon $-Nash equilibrium property is verified.

中文翻译：

---

线性二次高斯平均场博弈，具有部分观测和共同噪声

本文考虑了一类线性二次高斯（LQG）平均场博弈（MFG），其具有针对个体个体的部分观察结构。与其他文献不同，我们的配方具有某些特殊功能。首先，由于外部因素，单个状态由某种公共噪声驱动，因此状态平均成为随机过程，而不是确定的数量。其次，个体观察的传感器功能取决于状态平均值，因此，代理以三重方式耦合：不仅在其状态和成本功能上，而且还通过其观察机制。个体代理的分散策略是根据卡尔曼滤波和分离原理得出的。得到的一致性条件等效于由共同噪声驱动的一些前后向随机微分方程（FBSDE）的适定性。最后，验证了相关的\\ epsilon $ -Nash平衡性质。