Initial Error Affection and Error Correction in Linear Quadratic Mean Field Games under Erroneous Initial Information

In this paper, the initial error affection and error correction in linear quadratic mean field games (MPLQMFGs) under erroneous initial distribution information are investigated. First, a LQMFG model is developed where agents are coupled by dynamics and cost functions. Next, by studying the evolutionary of LQMFGs under erroneous initial distributions information, the affection of initial error on the game and agents' strategies are given. Furthermore, under deterministic situation, we provide a sufficient condition for agents to correct initial error and give their optimal strategies when agents are allowed to change their strategies at a intermediate time. Besides, the situation where agents are allowed to predict MF and adjust their strategies in real-time is considered. Finally, simulations are performed to verify above conclusions.