# Incentive Allocation in Vertical Federated Learning Based on Bankruptcy Problem

arXiv: https://arxiv.org/abs/2307.03515 · HTML: https://mlsanity.com/paper/2307.03515/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 7 Jul 2023.

## Builds on (most cited first, 13 of 13)

- [Towards Federated Learning at Scale: System Design](https://mlsanity.com/paper/1902.01046/) (2019)
- [Federated Machine Learning: Concept and Applications](https://mlsanity.com/paper/1902.04885/) (2019)
- [Federated Learning on Non-IID Data: A Survey](https://mlsanity.com/paper/2106.06843/) (2021)
- [A Survey on Distributed Machine Learning](https://mlsanity.com/paper/1912.09789/) (2019)
- [A Principled Approach to Data Valuation for Federated Learning](https://mlsanity.com/paper/2009.06192/) (2020)
- [The Shapley Value in Machine Learning](https://mlsanity.com/paper/2202.05594/) (2022)
- [Measure Contribution of Participants in Federated Learning](https://mlsanity.com/paper/1909.08525/) (2019)
- [GTG-Shapley: Efficient and Accurate Participant Contribution Evaluation in Federated Learning](https://mlsanity.com/paper/2109.02053/) (2021)
- [FMore: An Incentive Scheme of Multi-dimensional Auction for Federated Learning in MEC](https://mlsanity.com/paper/2002.09699/) (2020)
- [Motivating Workers in Federated Learning: A Stackelberg Game Perspective](https://mlsanity.com/paper/1908.03092/) (2019)
- [An Incentive Mechanism for Federated Learning in Wireless Cellular network: An Auction Approach](https://mlsanity.com/paper/2009.10269/) (2020)
- [Fair and efficient contribution valuation for vertical federated learning](https://mlsanity.com/paper/2201.02658/) (2022)
- [A Contract Theory based Incentive Mechanism for Federated Learning](https://mlsanity.com/paper/2108.05568/) (2021)

## Built on by (most cited first, 2 of 2)

- [A Survey on Contribution Evaluation in Vertical Federated Learning](https://mlsanity.com/paper/2405.02364/) (2024)
- [OPUS-VFL: Incentivizing Optimal Privacy-Utility Tradeoffs in Vertical Federated Learning](https://mlsanity.com/paper/2504.15995/) (2025)

## Abstract (arXiv)

Vertical federated learning (VFL) is a promising approach for collaboratively training machine learning models using private data partitioned vertically across different parties. Ideally in a VFL setting, the active party (party possessing features of samples with labels) benefits by improving its machine learning model through collaboration with some passive parties (parties possessing additional features of the same samples without labels) in a privacy preserving manner. However, motivating passive parties to participate in VFL can be challenging. In this paper, we focus on the problem of allocating incentives to the passive parties by the active party based on their contributions to the VFL process. We address this by formulating the incentive allocation problem as a bankruptcy game, a concept from cooperative game theory. Using the Talmudic division rule, which leads to the Nucleolus as its solution, we ensure a fair distribution of incentives. We evaluate our proposed method on synthetic and real-world datasets and show that it ensures fairness and stability in incentive allocation among passive parties who contribute their data to the federated model. Additionally, we compare our method to the existing solution of calculating Shapley values and show that our approach provides a more efficient solution with fewer computations.