# Fair Indivisible Payoffs through Shapley Value

arXiv: https://arxiv.org/abs/2510.24906 · HTML: https://mlsanity.com/paper/2510.24906/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 33 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Builds on (most cited first, 9 of 9)

- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Towards Unifying Feature Attribution and Counterfactual Explanations: Different Means to the Same End](https://mlsanity.com/paper/2011.04917/) (2020)
- [Multi-Winner Voting with Approval Preferences](https://mlsanity.com/paper/2007.01795/) (2020)
- [Robust and Verifiable Proportionality Axioms for Multiwinner Voting](https://mlsanity.com/paper/2302.01989/) (2023)
- [Democratic Fair Allocation of Indivisible Goods](https://mlsanity.com/paper/1709.02564/) (2017)
- [Approval-Based Apportionment](https://mlsanity.com/paper/1911.08365/) (2019)
- [The Complexity of Matching Games: A Survey](https://mlsanity.com/paper/2202.06898/) (2022)

## Abstract (arXiv)

We consider the problem of payoff division in indivisible coalitional games, where the value of the grand coalition is a natural number. This number represents a certain quantity of indivisible objects, such as parliamentary seats, kidney exchanges, or top features contributing to the outcome of a machine learning model. The goal of this paper is to propose a fair method for dividing these objects among players. To achieve this, we define the indivisible Shapley value and study its properties. We demonstrate our proposed technique using three case studies, in particular, we use it to identify key regions of an image in the context of an image classification task.