# Finite State Graphon Games with Applications to Epidemics

arXiv: https://arxiv.org/abs/2106.07859 · HTML: https://mlsanity.com/paper/2106.07859/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2021.

## Built on by (most cited first, 10 of 10)

- [Learning Graphon Mean Field Games and Approximate Nash Equilibria](https://mlsanity.com/paper/2112.01280/) (2021)
- [A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2209.03859/) (2022)
- [Learning Sparse Graphon Mean Field Games](https://mlsanity.com/paper/2209.03880/) (2022)
- [Learning Regularized Monotone Graphon Mean-Field Games](https://mlsanity.com/paper/2310.08089/) (2023)
- [Mean Field Games on Weighted and Directed Graphs via Colored Digraphons](https://mlsanity.com/paper/2209.03887/) (2022)
- [Reconciling Discrete-Time Mixed Policies and Continuous-Time Relaxed Controls in Reinforcement Learning and Stochastic Control](https://mlsanity.com/paper/2504.21793/) (2025)
- [Exploiting Approximate Symmetry for Efficient Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2408.15173/) (2024)
- [Reinforcement Learning for SBM Graphon Games with Re-Sampling](https://mlsanity.com/paper/2310.16326/) (2023)
- [A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agents](https://mlsanity.com/paper/2402.07365/) (2024)
- [Neural Parameter Calibration for Finite-State Mean Field Games](https://mlsanity.com/paper/2606.23155/) (2026)

## Abstract (arXiv)

We consider a game for a continuum of non-identical players evolving on a finite state space. Their heterogeneous interactions are represented by a graphon, which can be viewed as the limit of a dense random graph. The player's transition rates between the states depend on their own control and the interaction strengths with the other players. We develop a rigorous mathematical framework for this game and analyze Nash equilibria. We provide a sufficient condition for a Nash equilibrium and prove existence of solutions to a continuum of fully coupled forward-backward ordinary differential equations characterizing equilibria. Moreover, we propose a numerical approach based on machine learning tools and show experimental results on different applications to compartmental models in epidemiology.