# Multi-Agent Privacy Game in Federated Learning: A Unified Mean-Field View

arXiv: https://arxiv.org/abs/2607.23029 · HTML: https://mlsanity.com/paper/2607.23029/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 25 Jul 2026.

## Builds on (most cited first, 15 of 15)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Inverting Gradients -- How easy is it to break privacy in federated learning?](https://mlsanity.com/paper/2003.14053/) (2020)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Differentially Private Federated Learning: A Client Level Perspective](https://mlsanity.com/paper/1712.07557/) (2017)
- [Differentially Private Learning with Adaptive Clipping](https://mlsanity.com/paper/1905.03871/) (2019)
- [A Hybrid Approach to Privacy-Preserving Federated Learning](https://mlsanity.com/paper/1812.03224/) (2018)
- [Robust Federated Learning: The Case of Affine Distribution Shifts](https://mlsanity.com/paper/2006.08907/) (2020)
- [A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems](https://mlsanity.com/paper/1912.01825/) (2019)
- [Trading Data For Learning: Incentive Mechanism For On-Device Federated Learning](https://mlsanity.com/paper/2009.05604/) (2020)
- [Federated Learning as a Mean-Field Game](https://mlsanity.com/paper/2107.03770/) (2021)
- [Federated Learning with Differential Privacy](https://mlsanity.com/paper/2402.02230/) (2024)

## Abstract (arXiv)

Federated learning enables collaborative model training across distributed clients without centralising their data, yet privacy remains a persistent concern because the shared model updates can leak information about local datasets. Existing privacy-preserving methods either inject calibrated noise into client updates, limiting their composition guarantees, or formulate client privacy choices as a multi-agent game whose Nash equilibrium becomes intractable as the number of clients grows. We bridge these two lines of work by formulating privacy-preserving federated learning as a mean-field privacy game: each client strategically chooses its own privacy budget while interacting with the population only through a single mean-field statistic. The mean-field limit yields a tractable equilibrium for arbitrarily many clients, accommodates heterogeneous client preferences, and inherits an exponentially decaying privacy guarantee through a log-Sobolev contraction. The framework recovers the entropic privacy baseline as the homogeneous special case and the multi-agent privacy game as the finite-population case. Experiments on quadratic regression, logistic regression, and MNIST demonstrate that the proposed framework attains the privacy-utility trade-off of the entropic baseline while delivering a personalized privacy guarantee that the homogeneous baseline cannot express.