Fair Indivisible Payoffs through Shapley Value

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.

Miko\laj Czarnecki, Micha\l Korniak, Oskar Skibski, Piotr Skowron · 2025