# Graphon Mean Field Games and the GMFG Equations

arXiv: https://arxiv.org/abs/2008.10216 · HTML: https://mlsanity.com/paper/2008.10216/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Aug 2020.

## Built on by (most cited first, 13 of 13)

- [Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm](https://mlsanity.com/paper/2405.08005/) (2024)
- [Learning operators on labelled conditional distributions with applications to mean field control of non exchangeable systems](https://mlsanity.com/paper/2603.21683/) (2026)
- [Learning Mean Field Control on Sparse Graphs](https://mlsanity.com/paper/2501.17079/) (2025)
- [Reinforcement Learning for SBM Graphon Games with Re-Sampling](https://mlsanity.com/paper/2310.16326/) (2023)
- [Convergence and Connectivity: Dynamics of Multi-Agent Q-Learning in Random Networks](https://mlsanity.com/paper/2503.10186/) (2025)
- [Policy Optimization for Continuous-time Linear-Quadratic Graphon Mean Field Games](https://mlsanity.com/paper/2506.05894/) (2025)
- [Graphon Mean-Field Subsampling for Cooperative Heterogeneous Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2602.16196/) (2026)
- [Fixed-Point Centrality for Networks](https://mlsanity.com/paper/2209.07070/) (2022)
- [Sparse Mean Field Load Balancing in Large Localized Queueing Systems](https://mlsanity.com/paper/2312.12973/) (2023)
- [Graphon Particle Systems, Part II: Dynamics of Distributed Stochastic Continuum Optimization](https://mlsanity.com/paper/2407.02765/) (2024)
- [A Scalable Game Theoretic Approach for Coordination of Multiple Dynamic Systems](https://mlsanity.com/paper/2409.11358/) (2024)
- [Mean-Field Control on Sparse Graphs: From Local Limits to GNNs via Neighborhood Distributions](https://mlsanity.com/paper/2601.21477/) (2026)
- [Decentralized Strategies for Finite Population LQG Social Control: A Reinforcement Learning Approach](https://mlsanity.com/paper/2608.30244/) (2026)

## Abstract (arXiv)

The emergence of the graphon theory of large networks and their infinite limits has enabled the formulation of a theory of the centralized control of dynamical systems distributed on asymptotically infinite networks (Gao and Caines, IEEE CDC 2017, 2018). Furthermore, the study of the decentralized control of such systems was initiated in (Caines and Huang, IEEE CDC 2018, 2019), where Graphon Mean Field Games (GMFG) and the GMFG equations were formulated for the analysis of non-cooperative dynamic games on unbounded networks. In that work, existence and uniqueness results were introduced for the GMFG equations, together with an epsilon-Nash theory for GMFG systems which relates infinite population equilibria on infinite networks to finite population equilibria on finite networks. Those results are rigorously established in this paper.