# Nonlinear Equilibrium Transitions in a Potential Game Model for Federated Learning

arXiv: https://arxiv.org/abs/2411.11793 · HTML: https://mlsanity.com/paper/2411.11793/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 52 references that are in the map.
- First posted on arXiv 18 Nov 2024.

## Builds on (most cited first, 14 of 14)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Federated Learning for Mobile Keyboard Prediction](https://mlsanity.com/paper/1811.03604/) (2018)
- [Federated Learning for Edge Networks: Resource Optimization and Incentive Mechanism](https://mlsanity.com/paper/1911.05642/) (2019)
- [GTG-Shapley: Efficient and Accurate Participant Contribution Evaluation in Federated Learning](https://mlsanity.com/paper/2109.02053/) (2021)
- [Model-sharing Games: Analyzing Federated Learning Under Voluntary Participation](https://mlsanity.com/paper/2010.00753/) (2020)
- [Optimality and Stability in Federated Learning: A Game-theoretic Approach](https://mlsanity.com/paper/2106.09580/) (2021)
- [martFL: Enabling Utility-Driven Data Marketplace with a Robust and Verifiable Federated Learning Architecture](https://mlsanity.com/paper/2309.01098/) (2023)
- [Game Theoretic Control of Multi-Agent Systems](https://mlsanity.com/paper/1608.00192/) (2016)
- [Approximate Nash equilibria in large nonconvex aggregative games](https://mlsanity.com/paper/2011.12604/) (2020)
- [A Game-theoretic Framework for Privacy-preserving Federated Learning](https://mlsanity.com/paper/2304.05836/) (2023)

## Abstract (arXiv)

In federated learning (FL), a central server typically allocates training efforts to clients. However, from a market-oriented perspective, clients may independently choose their training efforts based on rational self-interest. To study this setting, we propose a potential game framework in which each client's payoff is determined by its individual effort and the rewards provided by the server. The rewards are influenced by the collective efforts of all clients and can be modulated by a reward factor. We first establish the existence of Nash equilibria (NEs) and then investigate their uniqueness in a stationary setting. We show that the NEs depend nonlinearly on the reward factor and exhibit a nonsmooth transition at a critical value, where the stationary potential loses strict curvature, leading to nonunique NEs and a jump between low-effort and high-effort branches. Furthermore, we prove the convergence of the best-response algorithm for computing NEs in our FL game. Finally, we apply the clients' rational efforts derived from the NEs to FL training with various datasets and models, thereby validating the effectiveness of the identified critical reward factor. The source code is available at https://github.com/DCN-FAU-AvH/FL-Potential-Game