Sensitivity Analysis for Network LQG Mean-Field Games: A Graphon Limit Approach

Abstract

This paper provides the sensitivity analysis of Linear Quadratic Gaussian graphon mean-field games (LQG-GMFG), with a particular focus on how perturbations in initial conditions at different network locations affect system behavior. We quantify the impact of localized perturbations through a L²-perturbation metric via graphon spectral decompositions and establish explicit solutions for the perturbation analysis that reveal how network topology influences perturbation propagation patterns. Our theoretical results reveal fundamental connections among network topology, system dynamics, and sensitivity patterns, providing insights for robust network design and control strategies.