# Model-sharing Games: Analyzing Federated Learning Under Voluntary Participation

arXiv: https://arxiv.org/abs/2010.00753 · HTML: https://mlsanity.com/paper/2010.00753/

## Key facts

- Cited by 60 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2020.

## Built on by (most cited first, 30 of 60)

- [Incentive Mechanisms for Federated Learning: From Economic and Game Theoretic Perspective](https://mlsanity.com/paper/2111.11850/) (2021)
- [A Survey on Heterogeneous Federated Learning](https://mlsanity.com/paper/2210.04505/) (2022)
- [Optimality and Stability in Federated Learning: A Game-theoretic Approach](https://mlsanity.com/paper/2106.09580/) (2021)
- [One for One, or All for All: Equilibria and Optimality of Collaboration in Federated Learning](https://mlsanity.com/paper/2103.03228/) (2021)
- [Mechanisms that Incentivize Data Sharing in Federated Learning](https://mlsanity.com/paper/2207.04557/) (2022)
- [Cross-Silo Federated Learning: Challenges and Opportunities](https://mlsanity.com/paper/2206.12949/) (2022)
- [Overcoming Data and Model Heterogeneities in Decentralized Federated Learning via Synthetic Anchors](https://mlsanity.com/paper/2405.11525/) (2024)
- [Optimizing the Collaboration Structure in Cross-Silo Federated Learning](https://mlsanity.com/paper/2306.06508/) (2023)
- [Fine-Tuning Games: Bargaining and Adaptation for General-Purpose Models](https://mlsanity.com/paper/2308.04399/) (2023)
- [Collaboration Equilibrium in Federated Learning](https://mlsanity.com/paper/2108.07926/) (2021)
- [DU-Shapley: A Shapley Value Proxy for Efficient Dataset Valuation](https://mlsanity.com/paper/2306.02071/) (2023)
- [WAFFLE: Weighted Averaging for Personalized Federated Learning](https://mlsanity.com/paper/2110.06978/) (2021)
- [Linear Speedup in Personalized Collaborative Learning](https://mlsanity.com/paper/2111.05968/) (2021)
- [Noise-Aware Algorithm for Heterogeneous Differentially Private Federated Learning](https://mlsanity.com/paper/2406.03519/) (2024)
- [Free-Rider and Conflict Aware Collaboration Formation for Cross-Silo Federated Learning](https://mlsanity.com/paper/2410.19321/) (2024)
- [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 Comprehensive Survey of Federated Transfer Learning: Challenges, Methods and Applications](https://mlsanity.com/paper/2403.01387/) (2024)
- [Optimal Model Averaging: Towards Personalized Collaborative Learning](https://mlsanity.com/paper/2110.12946/) (2021)
- [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)
- [Incentivizing Honesty among Competitors in Collaborative Learning and Optimization](https://mlsanity.com/paper/2305.16272/) (2023)
- [The Fair Value of Data Under Heterogeneous Privacy Constraints in Federated Learning](https://mlsanity.com/paper/2301.13336/) (2023)
- [Multiplayer Federated Learning: Reaching Equilibrium with Less Communication](https://mlsanity.com/paper/2501.08263/) (2025)
- [Truthful Incentive Mechanism for Federated Learning with Crowdsourced Data Labeling](https://mlsanity.com/paper/2302.00106/) (2023)
- [FedCompetitors: Harmonious Collaboration in Federated Learning with Competing Participants](https://mlsanity.com/paper/2312.11391/) (2023)
- [RobWE: Robust Watermark Embedding for Personalized Federated Learning Model Ownership Protection](https://mlsanity.com/paper/2402.19054/) (2024)
- [Collaborative Mean Estimation Among Heterogeneous Strategic Agents: Individual Rationality, Fairness, and Truthful Contribution](https://mlsanity.com/paper/2407.15881/) (2024)
- [Secure and Efficient Watermarking for Latent Diffusion Models in Model Distribution Scenarios](https://mlsanity.com/paper/2502.13345/) (2025)
- [Maximizing Global Model Appeal in Federated Learning](https://mlsanity.com/paper/2205.14840/) (2022)

## Abstract (arXiv)

Federated learning is a setting where agents, each with access to their own data source, combine models from local data to create a global model. If agents are drawing their data from different distributions, though, federated learning might produce a biased global model that is not optimal for each agent. This means that agents face a fundamental question: should they choose the global model or their local model? We show how this situation can be naturally analyzed through the framework of coalitional game theory. We propose the following game: there are heterogeneous players with different model parameters governing their data distribution and different amounts of data they have noisily drawn from their own distribution. Each player's goal is to obtain a model with minimal expected mean squared error (MSE) on their own distribution. They have a choice of fitting a model based solely on their own data, or combining their learned parameters with those of some subset of the other players. Combining models reduces the variance component of their error through access to more data, but increases the bias because of the heterogeneity of distributions. Here, we derive exact expected MSE values for problems in linear regression and mean estimation. We then analyze the resulting game in the framework of hedonic game theory; we study how players might divide into coalitions, where each set of players within a coalition jointly construct model(s). We analyze three methods of federation, modeling differing degrees of customization. In uniform federation, the agents collectively produce a single model. In coarse-grained federation, each agent can weight the global model together with their local model. In fine-grained federation, each agent can flexibly combine models from all other agents in the federation. For each method, we analyze the stable partitions of players into coalitions.