Initial Error Affection and Strategy Modification in Multi-Population LQ Mean Field Games under Erroneous Initial Distribution Information

In this paper, the initial error affection and strategy modification in multi-population linear quadratic mean field games (MPLQMFGs) under erroneous initial distribution information are investigated. First, a MPLQMFG model is developed where agents in different populations are coupled by dynamics and cost functions. Next, by studying the evolutionary of MPLQMFGs under erroneous initial distribution information, the predicted and the actual evolutionary of mean field states are given. Furthermore, assume that each agent maintains observations only of its own state and control as well as the mean field terms of its own population, and agents are allowed to modify their strategies at an intermediate moment, two sufficient conditions are provided, where the game will reach the Nash equilibrium under correct information. Besides, the affection of the initial error on the game is discussed. Finally, simulations on the opinion evolutions of two groups are performed to verify above conclusions.