# Synchronization in a Kuramoto Mean Field Game

arXiv: https://arxiv.org/abs/2210.12912 · HTML: https://mlsanity.com/paper/2210.12912/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2022.

## Built on by (most cited first, 4 of 4)

- [Learning Decentralized Partially Observable Mean Field Control for Artificial Collective Behavior](https://mlsanity.com/paper/2307.06175/) (2023)
- [Major-Minor Mean Field Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2303.10665/) (2023)
- [Learning Distributed Equilibria in Linear-Quadratic Stochastic Differential Games: An α-Potential Approach](https://mlsanity.com/paper/2602.16555/) (2026)
- [Functional role of synchronization: A mean-field control perspective](https://mlsanity.com/paper/2502.00590/) (2025)

## Abstract (arXiv)

The classical Kuramoto model is studied in the setting of an infinite horizon mean field game. The system is shown to exhibit both synchronization and phase transition. Incoherence below a critical value of the interaction parameter is demonstrated by the stability of the uniform distribution. Above this value, the game bifurcates and develops self-organizing time homogeneous Nash equilibria. As interactions become stronger, these stationary solutions become fully synchronized. Results are proved by an amalgam of techniques from nonlinear partial differential equations, viscosity solutions, stochastic optimal control and stochastic processes.