Linear Quadratic Mean Field Games under Heterogeneous Erroneous Initial Information

Abstract

In this paper, linear quadratic mean field games (LQMFGs) under heterogeneous erroneous initial information are investigated, focusing on how to achieve error correction by calculation based on the agents' own actual state and interactions in the game, rather than process observations. First, we establish a mathematic model for initial information error propagation in LQMFGs, several all-agents-known linear relationships between initial errors and deviations of agents' strategies and MF from those under correct information are given. Next, we investigate the error correction and strategy modification behavior of an agent and corresponding methods that only requires it own states. Under deterministic situation, a sufficient condition is provided for agents to compute actual MF and optimal strategies by one-time error correction, which is only related to modification time and parameters of the system. Under stochastic situation, the mathematical model of agents' real-time estimations for MF and corresponding strategies are given, and estimation error affections are analysed. Finally, simulations are performed to verify above conclusions.