# One for One, or All for All: Equilibria and Optimality of Collaboration in Federated Learning

arXiv: https://arxiv.org/abs/2103.03228 · HTML: https://mlsanity.com/paper/2103.03228/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 32 references that are in the map.
- First posted on arXiv 4 Mar 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Fair Resource Allocation in Federated Learning](https://mlsanity.com/paper/1905.10497/) (2019)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [EMNIST: an extension of MNIST to handwritten letters](https://mlsanity.com/paper/1702.05373/) (2017)
- [Collaborative Fairness in Federated Learning](https://mlsanity.com/paper/2008.12161/) (2020)
- [A Marketplace for Data: An Algorithmic Solution](https://mlsanity.com/paper/1805.08125/) (2018)
- [Collaborative Machine Learning with Incentive-Aware Model Rewards](https://mlsanity.com/paper/2010.12797/) (2020)
- [Model-sharing Games: Analyzing Federated Learning Under Voluntary Participation](https://mlsanity.com/paper/2010.00753/) (2020)
- [Free-riders in Federated Learning: Attacks and Defenses](https://mlsanity.com/paper/1911.12560/) (2019)
- [Hierarchically Fair Federated Learning](https://mlsanity.com/paper/2004.10386/) (2020)
- [Improved Algorithms for Collaborative PAC Learning](https://mlsanity.com/paper/1805.08356/) (2018)
- [Tight Bounds for Collaborative PAC Learning via Multiplicative Weights](https://mlsanity.com/paper/1805.09217/) (2018)
- [Statistical Cost Sharing](https://mlsanity.com/paper/1703.03111/) (2017)

## Built on by (most cited first, 30 of 39)

- [Optimality and Stability in Federated Learning: A Game-theoretic Approach](https://mlsanity.com/paper/2106.09580/) (2021)
- [On-Demand Sampling: Learning Optimally from Multiple Distributions](https://mlsanity.com/paper/2210.12529/) (2022)
- [Anchor Sampling for Federated Learning with Partial Client Participation](https://mlsanity.com/paper/2206.05891/) (2022)
- [Optimal Multi-Distribution Learning](https://mlsanity.com/paper/2312.05134/) (2023)
- [The sample complexity of multi-distribution learning](https://mlsanity.com/paper/2312.04027/) (2023)
- [Models of fairness in federated learning](https://mlsanity.com/paper/2112.00818/) (2021)
- [Fair yet Asymptotically Equal Collaborative Learning](https://mlsanity.com/paper/2306.05764/) (2023)
- [A Fair Federated Learning Framework With Reinforcement Learning](https://mlsanity.com/paper/2205.13415/) (2022)
- [Strategic Data Sharing between Competitors](https://mlsanity.com/paper/2305.16052/) (2023)
- [Scaff-PD: Communication Efficient Fair and Robust Federated Learning](https://mlsanity.com/paper/2307.13381/) (2023)
- [On the Effect of Defections in Federated Learning and How to Prevent Them](https://mlsanity.com/paper/2311.16459/) (2023)
- [Multiplayer Federated Learning: Reaching Equilibrium with Less Communication](https://mlsanity.com/paper/2501.08263/) (2025)
- [Probably Approximately Correct Federated Learning](https://mlsanity.com/paper/2304.04641/) (2023)
- [Collaborative Mean Estimation Among Heterogeneous Strategic Agents: Individual Rationality, Fairness, and Truthful Contribution](https://mlsanity.com/paper/2407.15881/) (2024)
- [Maximizing Global Model Appeal in Federated Learning](https://mlsanity.com/paper/2205.14840/) (2022)
- [FACT or Fiction: Can Truthful Mechanisms Eliminate Federated Free Riding?](https://mlsanity.com/paper/2405.13879/) (2024)
- [Incentivizing Truthful Collaboration in Heterogeneous Federated Learning](https://mlsanity.com/paper/2412.00980/) (2024)
- [The Backfiring Effect of Weak AI Safety Regulation](https://mlsanity.com/paper/2503.20848/) (2025)
- [How to Collaborate: Towards Maximizing the Generalization Performance in Cross-Silo Federated Learning](https://mlsanity.com/paper/2401.13236/) (2024)
- [Incentivized Truthful Communication for Federated Bandits](https://mlsanity.com/paper/2402.04485/) (2024)
- [Provable Mutual Benefits from Federated Learning in Privacy-Sensitive Domains](https://mlsanity.com/paper/2403.06672/) (2024)
- [Inference Attacks: A Taxonomy, Survey, and Promising Directions](https://mlsanity.com/paper/2406.02027/) (2024)
- [Long-term Data Sharing under Exclusivity Attacks](https://mlsanity.com/paper/2201.09137/) (2022)
- [Federated Learning as a Network Effects Game](https://mlsanity.com/paper/2302.08533/) (2023)
- [Dynamic Fair Federated Learning Based on Reinforcement Learning](https://mlsanity.com/paper/2311.00959/) (2023)
- [Cross-Silo Federated Learning Across Divergent Domains with Iterative Parameter Alignment](https://mlsanity.com/paper/2311.04818/) (2023)
- [Online Federation For Mixtures of Proprietary Agents with Black-Box Encoders](https://mlsanity.com/paper/2505.00216/) (2025)
- [Incentivize Contribution and Learn Parameters Too: Federated Learning with Strategic Data Owners](https://mlsanity.com/paper/2505.12010/) (2025)
- [Incentivized Collaboration in Active Learning](https://mlsanity.com/paper/2311.00260/) (2023)
- [Sample Complexity of Linear Regression Models for Opinion Formation in Networks](https://mlsanity.com/paper/2311.02349/) (2023)

## Abstract (arXiv)

In recent years, federated learning has been embraced as an approach for bringing about collaboration across large populations of learning agents. However, little is known about how collaboration protocols should take agents' incentives into account when allocating individual resources for communal learning in order to maintain such collaborations. Inspired by game theoretic notions, this paper introduces a framework for incentive-aware learning and data sharing in federated learning. Our stable and envy-free equilibria capture notions of collaboration in the presence of agents interested in meeting their learning objectives while keeping their own sample collection burden low. For example, in an envy-free equilibrium, no agent would wish to swap their sampling burden with any other agent and in a stable equilibrium, no agent would wish to unilaterally reduce their sampling burden. In addition to formalizing this framework, our contributions include characterizing the structural properties of such equilibria, proving when they exist, and showing how they can be computed. Furthermore, we compare the sample complexity of incentive-aware collaboration with that of optimal collaboration when one ignores agents' incentives.