mlsanityData to 14 Oct 2026

Enabling Long-Term Cooperation in Cross-Silo Federated Learning: A Repeated Game Perspective

arXiv 2106.11814 ↗First posted 22 Jun 2021cs.LG cs.GTcited by 14

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Abstract (arXiv)

Cross-silo federated learning (FL) is a distributed learning approach where clients of the same interest train a global model cooperatively while keeping their local data private. The success of a cross-silo FL process requires active participation of many clients. Clients in cross-silo FL aim to optimize their long-term benefits by selfishly choosing their participation levels. While there has been some work on incentivizing clients to join FL, the analysis of clients' long-term selfish participation behaviors in cross-silo FL remains largely unexplored. In this paper, we analyze the selfish participation behaviors of heterogeneous clients in cross-silo FL. Specifically, we model clients' long-term selfish participation behaviors as an infinitely repeated game. For the stage game SPFL, we derive the unique Nash equilibrium (NE), and propose a distributed algorithm for each client to calculate its equilibrium participation strategy. We show that at the NE, clients fall into at most three categories: (i) free riders, (ii) a unique partial contributor (if exists), and (iii) contributors. For the long-term interactions among clients, we derive a cooperative strategy for clients which minimizes the number of free riders while increasing the amount of local data for model training. We show that enforced by a punishment strategy, such a cooperative strategy is a subgame perfect Nash equilibrium (SPNE) of the infinitely repeated game, under which some clients who are free riders at the NE of the stage game choose to be (partial) contributors. We further propose an algorithm to calculate the optimal SPNE which minimizes the number of free riders while maximizing the amount of local data for model training. Simulation results show that our derived optimal SPNE can effectively reduce the number of free riders by up to 99.3% and increase the amount of local data for model training by up to 82.3%.

Key facts. Cited by 14 papers in the map (data through 14 Oct 2026). Builds on 25 of its 68 references that are in the map. First posted on arXiv 22 Jun 2021.

Builds on

25 of 68 references.

References · 25

  1. 2016Communication-Efficient Learning of Deep Networks from Decentralized Datacited by 7,669
  2. 2019Advances and Open Problems in Federated Learningcited by 3,046
  3. 2019On the Convergence of FedAvg on Non-IID Datacited by 1,229
  4. 2019Agnostic Federated Learningcited by 456
  5. 2018Adaptive Federated Learning in Resource Constrained Edge Computing Systemscited by 409
  6. 2019Federated Learning in Mobile Edge Networks: A Comprehensive Surveycited by 408
  7. 2020Personalized Cross-Silo Federated Learning on Non-IID Datacited by 283
  8. 2018Broadband Analog Aggregation for Low-Latency Federated Edge Learning (Extended Version)cited by 191
  9. 2020Federated Learning for Internet of Things: Recent Advances, Taxonomy, and Open Challengescited by 139
  10. 2020Cost-Effective Federated Learning Designcited by 62
  11. 2020Free-rider Attacks on Model Aggregation in Federated Learningcited by 57
  12. 2019Free-riders in Federated Learning: Attacks and Defensescited by 49
13 more
  1. 2020FMore: An Incentive Scheme of Multi-dimensional Auction for Federated Learning in MECcited by 48
  2. 2021Device Sampling for Heterogeneous Federated Learning: Theory, Algorithms, and Implementationcited by 40
  3. 2020Throughput-Optimal Topology Design for Cross-Silo Federated Learningcited by 39
  4. 2020FOCUS: Dealing with Label Quality Disparity in Federated Learningcited by 36
  5. 2020Energy-Efficient Federated Edge Learning with Joint Communication and Computation Designcited by 30
  6. 2020Adaptive Federated Learning With Gradient Compression in Uplink NOMAcited by 19
  7. 2020An Exploratory Analysis on Users' Contributions in Federated Learningcited by 15
  8. 2021Towards Causal Federated Learning For Enhanced Robustness and Privacycited by 14
  9. 2020Communication Efficient Federated Learning over Multiple Access Channelscited by 11
  10. 2020Differentially private cross-silo federated learningcited by 7
  11. 2019Network Utility Maximization based on Incentive Mechanism for Truthful Reporting of Local Informationcited by 4
  12. 2013Demand Side Management in Smart Grids using a Repeated Game Frameworkcited by 1
  13. 2021Reputation and Pricing Dynamics in Online Marketscited by 1

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Citing papers per year: 2022: 2; 2023: 8; 2024: 0; 2025: 4.

14 papers.

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  1. 2022Mechanisms that Incentivize Data Sharing in Federated Learningcited by 39
  2. 2023Evaluating and Incentivizing Diverse Data Contributions in Collaborative Learningcited by 8
  3. 2023Fair yet Asymptotically Equal Collaborative Learningcited by 8
  4. 2023On the Effect of Defections in Federated Learning and How to Prevent Themcited by 5
  5. 2025Research in Collaborative Learning Does Not Serve Cross-Silo Federated Learning in Practicecited by 3
  6. 2023Welfare and Fairness Dynamics in Federated Learning: A Client Selection Perspectivecited by 1
  7. 2023Learner Referral for Cost-Effective Federated Learning Over Hierarchical IoT Networkscited by 1
  8. 2022GTFLAT: Game Theory Based Add-On For Empowering Federated Learning Aggregation Techniquescited by 0
  9. 2023Adaptive incentive for cross-silo federated learning: A multi-agent reinforcement learning approachcited by 0
  10. 2023Price of Stability in Quality-Aware Federated Learningcited by 0
  11. 2023Incentive Mechanism Design for Distributed Ensemble Learningcited by 0
  12. 2025TACO: Tackling Over-correction in Federated Learning with Tailored Adaptive Correctioncited by 0
2 more
  1. 2025Degree of Staleness-Aware Data Updating in Federated Learningcited by 0
  2. 2025Gaming and Cooperation in Federated Learning: What Can Happen and How to Monitor Itcited by 0