# Free-Rider Games for Federated Learning with Selfish Clients in NextG Wireless Networks

arXiv: https://arxiv.org/abs/2212.11194 · HTML: https://mlsanity.com/paper/2212.11194/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 27 references that are in the map.
- First posted on arXiv 21 Dec 2022.

## Builds on (most cited first, 21 of 21)

- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Towards Federated Learning at Scale: System Design](https://mlsanity.com/paper/1902.01046/) (2019)
- [Federated Learning in Mobile Edge Networks: A Comprehensive Survey](https://mlsanity.com/paper/1909.11875/) (2019)
- [Analyzing Federated Learning through an Adversarial Lens](https://mlsanity.com/paper/1811.12470/) (2018)
- [A Joint Learning and Communications Framework for Federated Learning over Wireless Networks](https://mlsanity.com/paper/1909.07972/) (2019)
- [Threats to Federated Learning: A Survey](https://mlsanity.com/paper/2003.02133/) (2020)
- [Federated Learning for Internet of Things: Recent Advances, Taxonomy, and Open Challenges](https://mlsanity.com/paper/2009.13012/) (2020)
- [Federated Learning for Wireless Communications: Motivation, Opportunities and Challenges](https://mlsanity.com/paper/1908.06847/) (2019)
- [Distributed Learning in Wireless Networks: Recent Progress and Future Challenges](https://mlsanity.com/paper/2104.02151/) (2021)
- [Federated Learning for Edge Networks: Resource Optimization and Incentive Mechanism](https://mlsanity.com/paper/1911.05642/) (2019)
- [Free-rider Attacks on Model Aggregation in Federated Learning](https://mlsanity.com/paper/2006.11901/) (2020)
- [Free-riders in Federated Learning: Attacks and Defenses](https://mlsanity.com/paper/1911.12560/) (2019)
- [Incentive Mechanisms for Federated Learning: From Economic and Game Theoretic Perspective](https://mlsanity.com/paper/2111.11850/) (2021)
- [Optimality and Stability in Federated Learning: A Game-theoretic Approach](https://mlsanity.com/paper/2106.09580/) (2021)
- [Deep Learning for Wireless Communications](https://mlsanity.com/paper/2005.06068/) (2020)
- [A Secure Federated Learning Framework for 5G Networks](https://mlsanity.com/paper/2005.05752/) (2020)
- [Deep Learning for RF Signal Classification in Unknown and Dynamic Spectrum Environments](https://mlsanity.com/paper/1909.11800/) (2019)
- [Federated Learning for Distributed Spectrum Sensing in NextG Communication Networks](https://mlsanity.com/paper/2204.03027/) (2022)
- [Jamming Attacks on Federated Learning in Wireless Networks](https://mlsanity.com/paper/2201.05172/) (2022)
- [Secure Federated Learning in 5G Mobile Networks](https://mlsanity.com/paper/2004.06700/) (2020)

## Built on by (most cited first, 6 of 6)

- [Jamming Attacks on Decentralized Federated Learning in General Multi-Hop Wireless Networks](https://mlsanity.com/paper/2301.05250/) (2023)
- [Tackling Selfish Clients in Federated Learning](https://mlsanity.com/paper/2407.15402/) (2024)
- [Securing NextG Systems against Poisoning Attacks on Federated Learning: A Game-Theoretic Solution](https://mlsanity.com/paper/2312.17164/) (2023)
- [Gaming and Cooperation in Federated Learning: What Can Happen and How to Monitor It](https://mlsanity.com/paper/2509.02391/) (2025)
- [Reputation-driven Cooperation in Lattice-based Decentralized Federated Learning through Evolutionary Game Theory](https://mlsanity.com/paper/2608.01197/) (2026)
- [Upholding Robustness in Federated Learning: Trends, Emerging Strategies, and Research Opportunities](https://mlsanity.com/paper/2609.28722/) (2026)

## Abstract (arXiv)

This paper presents a game theoretic framework for participation and free-riding in federated learning (FL), and determines the Nash equilibrium strategies when FL is executed over wireless links. To support spectrum sensing for NextG communications, FL is used by clients, namely spectrum sensors with limited training datasets and computation resources, to train a wireless signal classifier while preserving privacy. In FL, a client may be free-riding, i.e., it does not participate in FL model updates, if the computation and transmission cost for FL participation is high, and receives the global model (learned by other clients) without incurring a cost. However, the free-riding behavior may potentially decrease the global accuracy due to lack of contribution to global model learning. This tradeoff leads to a non-cooperative game where each client aims to individually maximize its utility as the difference between the global model accuracy and the cost of FL participation. The Nash equilibrium strategies are derived for free-riding probabilities such that no client can unilaterally increase its utility given the strategies of its opponents remain the same. The free-riding probability increases with the FL participation cost and the number of clients, and a significant optimality gap exists in Nash equilibrium with respect to the joint optimization for all clients. The optimality gap increases with the number of clients and the maximum gap is evaluated as a function of the cost. These results quantify the impact of free-riding on the resilience of FL in NextG networks and indicate operational modes for FL participation.