Linear-Quadratic Graphon Mean Field Games with Common Noise
Abstract
This paper studies linear quadratic graphon mean field games (LQ-GMFGs) with common noise, in which a large number of agents are coupled via a weighted undirected graph. One special feature, compared with the well-studied graphon mean field games, is that the states of agents are described by the dynamic systems with the idiosyncratic noises and common noise. The limit LQ-GMFGs with common noise are formulated based on the assumption that these graphs lie in a sequence converging to a limit graphon. By applying the spectral decomposition method, the existence of solution for the formulated limit LQ-GMFGs is derived. Moreover, based on the adequate convergence assumptions, a set of -Nash equilibrium strategies for the finite large population problem is constructed.
Cite
@article{arxiv.2401.09030,
title = {Linear-Quadratic Graphon Mean Field Games with Common Noise},
author = {De-xuan Xu and Zhun Gou and Nan-jing Huang and Shuang Gao},
journal= {arXiv preprint arXiv:2401.09030},
year = {2025}
}