Linear Quadratic Mean Field Games under Heterogeneous Erroneous Initial Information

TL;DR

This paper studies how agents in linear quadratic mean field games can correct errors in initial information using their own states, providing models and conditions for error correction in both deterministic and stochastic settings.

Contribution

It introduces a mathematical model for initial error propagation in LQMFGs and proposes methods for agents to correct errors using only their own states, with conditions for successful correction.

Findings

Error correction is feasible through one-time adjustment under deterministic conditions.

Agents can estimate mean field and strategies in real-time despite initial errors.

Simulations confirm the effectiveness of the proposed error correction methods.

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.