# Hypergraphon Mean Field Games

arXiv: https://arxiv.org/abs/2203.16223 · HTML: https://mlsanity.com/paper/2203.16223/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 83 references that are in the map.
- First posted on arXiv 30 Mar 2022.

## Builds on (most cited first, 29 of 29)

- [Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms](https://mlsanity.com/paper/1911.10635/) (2019)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [Multilayer Networks](https://mlsanity.com/paper/1309.7233/) (2013)
- [Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learning](https://mlsanity.com/paper/2102.01585/) (2021)
- [What are higher-order networks?](https://mlsanity.com/paper/2104.11329/) (2021)
- [Model-Free Mean-Field Reinforcement Learning: Mean-Field MDP and Mean-Field Q-Learning](https://mlsanity.com/paper/1910.12802/) (2019)
- [Entropy Regularization for Mean Field Games with Learning](https://mlsanity.com/paper/2010.00145/) (2020)
- [Mean-Field Controls with Q-learning for Cooperative MARL: Convergence and Complexity Analysis](https://mlsanity.com/paper/2002.04131/) (2020)
- [On the Convergence of Model Free Learning in Mean Field Games](https://mlsanity.com/paper/1907.02633/) (2019)
- [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)
- [Multi-Agent Reinforcement Learning in Stochastic Networked Systems](https://mlsanity.com/paper/2006.06555/) (2020)
- [Scaling up Mean Field Games with Online Mirror Descent](https://mlsanity.com/paper/2103.00623/) (2021)
- [On the Approximation of Cooperative Heterogeneous Multi-Agent Reinforcement Learning (MARL) using Mean Field Control (MFC)](https://mlsanity.com/paper/2109.04024/) (2021)
- [Markov-Nash Equilibria in Mean-Field Games with Discounted Cost](https://mlsanity.com/paper/1612.07878/) (2016)
- [Generalization in Mean Field Games by Learning Master Policies](https://mlsanity.com/paper/2109.09717/) (2021)
- [A General Framework for Learning Mean-Field Games](https://mlsanity.com/paper/2003.06069/) (2020)
- [Bellman equation and viscosity solutions for mean-field stochastic control problem](https://mlsanity.com/paper/1512.07866/) (2015)
- [Mean-Field-Type Games in Engineering](https://mlsanity.com/paper/1605.03281/) (2016)
- [Exploiting Fast Decaying and Locality in Multi-Agent MDP with Tree Dependence Structure](https://mlsanity.com/paper/1909.06900/) (2019)
- [Discrete-Time Mean Field Control with Environment States](https://mlsanity.com/paper/2104.14900/) (2021)
- [Solving N-player dynamic routing games with congestion: a mean field approach](https://mlsanity.com/paper/2110.11943/) (2021)
- [Mean-field type modeling of nonlocal crowd aversion in pedestrian crowd dynamics](https://mlsanity.com/paper/1701.09118/) (2017)
- [Can Mean Field Control (MFC) Approximate Cooperative Multi Agent Reinforcement Learning (MARL) with Non-Uniform Interaction?](https://mlsanity.com/paper/2203.00035/) (2022)
- [Linearly Solvable Mean-Field Traffic Routing Games](https://mlsanity.com/paper/1903.01449/) (2019)
- [Team Optimal Control of Coupled Subsystems with Mean-Field Sharing](https://mlsanity.com/paper/2012.01418/) (2020)
- [Dynamic driving and routing games for autonomous vehicles on networks: A mean field game approach](https://mlsanity.com/paper/2012.08388/) (2020)
- [Nonlinearity + Networks: A 2020 Vision](https://mlsanity.com/paper/1911.03805/) (2019)
- [Optimal Patching in Clustered Malware Epidemics](https://mlsanity.com/paper/1403.1639/) (2014)

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

- [A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2209.03859/) (2022)
- [Population-size-Aware Policy Optimization for Mean-Field Games](https://mlsanity.com/paper/2302.03364/) (2023)
- [Learning Mean Field Games on Sparse Graphs: A Hybrid Graphex Approach](https://mlsanity.com/paper/2401.12686/) (2024)

## Abstract (arXiv)

We propose an approach to modelling large-scale multi-agent dynamical systems allowing interactions among more than just pairs of agents using the theory of mean field games and the notion of hypergraphons, which are obtained as limits of large hypergraphs. To the best of our knowledge, ours is the first work on mean field games on hypergraphs. Together with an extension to a multi-layer setup, we obtain limiting descriptions for large systems of non-linear, weakly-interacting dynamical agents. On the theoretical side, we prove the well-foundedness of the resulting hypergraphon mean field game, showing both existence and approximate Nash properties. On the applied side, we extend numerical and learning algorithms to compute the hypergraphon mean field equilibria. To verify our approach empirically, we consider a social rumor spreading model, where we give agents intrinsic motivation to spread rumors to unaware agents, and an epidemics control problem.