2026/05/26 by Yuxin Jin, Haotian Wang, Wang Yao +1
#math.OC #math.PR
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.