AI 中文总结
研究具有错误初始信息的主次线性二次平均场博弈，通过构建最大似然估计器识别误差，提出基于估计的策略修正，刻画估计误差，表明主要智能体估计精度取决于观测到的次要智能体数量，数值结果验证了方法。
AI 中文摘要
本文研究了在受限观测结构下具有错误初始信息的主次线性二次平均场博弈（MMLQMFGs）。每个次要智能体仅观测自身状态和主要智能体的状态，而主要智能体观测自身状态和部分次要智能体的状态，双方均不直接观测平均场状态。研究表明初始信息误差通过博弈动态线性传播，导致主要状态、实际平均场及智能体内更新的平均场状态出现明显偏差。基于此结构，将分布式误差识别表述为离散时间局部观测的参数估计问题并构建未知初始误差的最大似然估计器。然后通过从估计误差重构当前平均场并切换到相应控制律，在中间时刻提出基于估计的策略修正。还刻画了所得估计误差，表明在当前对称设置下，主要智能体的估计精度取决于观测到的次要智能体数量而非其身份。数值结果说明了所提方法。
英文摘要
This paper studies major-minor linear-quadratic mean field games (MMLQMFGs) with erroneous initial information under a constrained observation structure. Each minor agent observes only its own state and the major agent's state, while the major agent observes its own state and the states of a subset of minor agents; neither side observes the mean field state directly. We show that the initial-information errors propagate linearly through the game dynamics and lead to explicit deviations in the major state, the actual mean field, and the agents' internally updated mean field states. Based on this structure, we formulate distributed error identification as a parameter-estimation problem from discrete-time local observations and construct maximum-likelihood estimators for unknown initial errors. We then propose an estimate-based strategy modification at an intermediate time by reconstructing the current mean field from the estimated errors and switching to the corresponding control law. We also characterize the resulting estimation errors and show that, in the present symmetric setting, the major agent's estimation precision depends on the number of observed minor agents but not on their identities. Numerical results illustrate the proposed method.
