# Stochastic Graphon Games: I. The Static Case

arXiv: https://arxiv.org/abs/1911.10664 · HTML: https://mlsanity.com/paper/1911.10664/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2019.

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

- [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)
- [Unified continuous-time q-learning for mean-field game and mean-field control problems](https://mlsanity.com/paper/2407.04521/) (2024)
- [Learning Regularized Monotone Graphon Mean-Field Games](https://mlsanity.com/paper/2310.08089/) (2023)
- [Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm](https://mlsanity.com/paper/2405.08005/) (2024)
- [Reconciling Discrete-Time Mixed Policies and Continuous-Time Relaxed Controls in Reinforcement Learning and Stochastic Control](https://mlsanity.com/paper/2504.21793/) (2025)
- [Reinforcement Learning for SBM Graphon Games with Re-Sampling](https://mlsanity.com/paper/2310.16326/) (2023)
- [Scalable Offline Reinforcement Learning for Mean Field Games](https://mlsanity.com/paper/2410.17898/) (2024)
- [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)
- [Directed Chain Generative Adversarial Networks](https://mlsanity.com/paper/2304.13131/) (2023)
- [A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agents](https://mlsanity.com/paper/2402.07365/) (2024)

## Abstract (arXiv)

We consider static finite-player network games and their continuum analogs, graphon games. Existence and uniqueness results are provided, as well as convergence of the finite-player network game optimal strategy profiles to their analogs for the graphon games. We also show that equilibrium strategy profiles of a graphon game provide approximate Nash equilibria for the finite-player games. Connections with mean field games and central planner optimization problems are discussed. Motivating applications are presented and explicit computations of their Nash equilibria and social optimal strategies are provided.