Nonlinear Equilibrium Transitions in a Potential Game Model for Federated Learning

Kang Liu, Ziqi Wang, and Enrique Zuazua

Overview

This repository contains the implementation code for the paper "Nonlinear Equilibrium Transitions in a Potential Game Model for Federated Learning."

Usage

First, run main_game.py to compute the Nash equilibrium of the FL-Game under different reward factors.

python main_game.py --m 1000

The four cases involving critical reward factors will be saved in the .\utils directory.

Then, to evaluate the FL training performance, execute main_train.py with the case argument from 1 to 4.

python main_train.py --m 1000 --case 1

All results and plots will be saved in the results folder.

Citation

If this code is useful for your research, please cite the paper:

@article{lwz2026FLGame,
title = {Nonlinear Equilibrium Transitions in a Potential Game Model for Federated Learning},
journal = {Physica D: Nonlinear Phenomena},
pages = {135288},
year = {2026},
issn = {0167-2789},
author = {Kang Liu and Ziqi Wang and Enrique Zuazua}
}

Acknowledgments

Alphabetical authorship according to mathematical tradition. Funded by the European Union's Horizon Europe MSCA project ModConFlex (grant number 101073558)