Fair Indivisible Payoffs through Shapley Value

TL;DR

This paper introduces an indivisible Shapley value for fair payoff division in coalitional games involving indivisible objects, with applications in areas like parliamentary seats, kidney exchanges, and machine learning feature attribution.

Contribution

It proposes a novel fair division method called the indivisible Shapley value and analyzes its properties and applications across multiple case studies.

Findings

The indivisible Shapley value provides a fair division approach for indivisible objects.

Case studies demonstrate its effectiveness in real-world scenarios.

The method helps identify key features in image classification tasks.

Abstract

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.