Hypergraphon Mean Field Games
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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.
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
29 of 83 references.
References · 29
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- 2022Scalable Deep Reinforcement Learning Algorithms for Mean Field Gamescited by 38
- 2020Multi-Agent Reinforcement Learning in Stochastic Networked Systemscited by 32
17 more
- 2021Scaling up Mean Field Games with Online Mirror Descentcited by 32
- 2021On the Approximation of Cooperative Heterogeneous Multi-Agent Reinforcement Learning (MARL) using Mean Field Control (MFC)cited by 32
- 2016Markov-Nash Equilibria in Mean-Field Games with Discounted Costcited by 31
- 2021Generalization in Mean Field Games by Learning Master Policiescited by 28
- 2020A General Framework for Learning Mean-Field Gamescited by 25
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- 2016Mean-Field-Type Games in Engineeringcited by 11
- 2019Exploiting Fast Decaying and Locality in Multi-Agent MDP with Tree Dependence Structurecited by 8
- 2021Discrete-Time Mean Field Control with Environment Statescited by 7
- 2021Solving N-player dynamic routing games with congestion: a mean field approachcited by 7
- 2017Mean-field type modeling of nonlocal crowd aversion in pedestrian crowd dynamicscited by 6
- 2022Can Mean Field Control (MFC) Approximate Cooperative Multi Agent Reinforcement Learning (MARL) with Non-Uniform Interaction?cited by 6
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- 2020Team Optimal Control of Coupled Subsystems with Mean-Field Sharingcited by 5
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- 2014Optimal Patching in Clustered Malware Epidemicscited by 2
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Citing papers per year: 2022: 1; 2023: 1; 2024: 1.
3 papers.