# Linear-Quadratic Graphon Mean Field Games with Common Noise

arXiv: https://arxiv.org/abs/2401.09030 · HTML: https://mlsanity.com/paper/2401.09030/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2024.

## Built on by (most cited first, 1 of 1)

- [Policy Optimization for Continuous-time Linear-Quadratic Graphon Mean Field Games](https://mlsanity.com/paper/2506.05894/) (2025)

## Abstract (arXiv)

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 ε-Nash equilibrium strategies for the finite large population problem is constructed.