# Learning Mean Field Games on Sparse Graphs: A Hybrid Graphex Approach

arXiv: https://arxiv.org/abs/2401.12686 · HTML: https://mlsanity.com/paper/2401.12686/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 52 references that are in the map.
- First posted on arXiv 23 Jan 2024.

## Builds on (most cited first, 19 of 19)

- [Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms](https://mlsanity.com/paper/1911.10635/) (2019)
- [Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learning](https://mlsanity.com/paper/2102.01585/) (2021)
- [Fictitious Play for Mean Field Games: Continuous Time Analysis and Applications](https://mlsanity.com/paper/2007.03458/) (2020)
- [Learning in Mean Field Games: A Survey](https://mlsanity.com/paper/2205.12944/) (2022)
- [Entropy Regularization for Mean Field Games with Learning](https://mlsanity.com/paper/2010.00145/) (2020)
- [On the Convergence of Model Free Learning in Mean Field Games](https://mlsanity.com/paper/1907.02633/) (2019)
- [Q-Learning in Regularized Mean-field Games](https://mlsanity.com/paper/2003.12151/) (2020)
- [Learning in Mean Field Games: the Fictitious Play](https://mlsanity.com/paper/1507.06280/) (2015)
- [Scalable Deep Reinforcement Learning Algorithms for Mean Field Games](https://mlsanity.com/paper/2203.11973/) (2022)
- [Mean Field Games Flock! The Reinforcement Learning Way](https://mlsanity.com/paper/2105.07933/) (2021)
- [Learning Graphon Mean Field Games and Approximate Nash Equilibria](https://mlsanity.com/paper/2112.01280/) (2021)
- [Sparse graphs using exchangeable random measures](https://mlsanity.com/paper/1401.1137/) (2014)
- [The Class of Random Graphs Arising from Exchangeable Random Measures](https://mlsanity.com/paper/1512.03099/) (2015)
- [Learning Sparse Graphon Mean Field Games](https://mlsanity.com/paper/2209.03880/) (2022)
- [Signatured Deep Fictitious Play for Mean Field Games with Common Noise](https://mlsanity.com/paper/2106.03272/) (2021)
- [Optimal incentives to mitigate epidemics: a Stackelberg mean field game approach](https://mlsanity.com/paper/2011.03105/) (2020)
- [Hypergraphon Mean Field Games](https://mlsanity.com/paper/2203.16223/) (2022)
- [Controlling Propagation of epidemics via mean-field control](https://mlsanity.com/paper/2006.01249/) (2020)
- [Mean-field games of speedy information access with observation costs](https://mlsanity.com/paper/2309.07877/) (2023)

## Built on by (most cited first, 3 of 3)

- [Learning Mean Field Control on Sparse Graphs](https://mlsanity.com/paper/2501.17079/) (2025)
- [Mean-Field Reinforcement Learning without Synchrony](https://mlsanity.com/paper/2602.18026/) (2026)
- [Mean-Field Control on Sparse Graphs: From Local Limits to GNNs via Neighborhood Distributions](https://mlsanity.com/paper/2601.21477/) (2026)

## Abstract (arXiv)

Learning the behavior of large agent populations is an important task for numerous research areas. Although the field of multi-agent reinforcement learning (MARL) has made significant progress towards solving these systems, solutions for many agents often remain computationally infeasible and lack theoretical guarantees. Mean Field Games (MFGs) address both of these issues and can be extended to Graphon MFGs (GMFGs) to include network structures between agents. Despite their merits, the real world applicability of GMFGs is limited by the fact that graphons only capture dense graphs. Since most empirically observed networks show some degree of sparsity, such as power law graphs, the GMFG framework is insufficient for capturing these network topologies. Thus, we introduce the novel concept of Graphex MFGs (GXMFGs) which builds on the graph theoretical concept of graphexes. Graphexes are the limiting objects to sparse graph sequences that also have other desirable features such as the small world property. Learning equilibria in these games is challenging due to the rich and sparse structure of the underlying graphs. To tackle these challenges, we design a new learning algorithm tailored to the GXMFG setup. This hybrid graphex learning approach leverages that the system mainly consists of a highly connected core and a sparse periphery. After defining the system and providing a theoretical analysis, we state our learning approach and demonstrate its learning capabilities on both synthetic graphs and real-world networks. This comparison shows that our GXMFG learning algorithm successfully extends MFGs to a highly relevant class of hard, realistic learning problems that are not accurately addressed by current MARL and MFG methods.