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.

翻译：本文研究不可分割联盟博弈中的收益分配问题，其中大联盟的价值为自然数。该数值代表特定数量的不可分割对象，例如议会席位、肾脏交换匹配或影响机器学习模型结果的关键特征。本文旨在提出一种公平分配这些对象给参与者的方法。为实现这一目标，我们定义了不可分割Shapley值并研究其性质。通过三个案例研究展示所提技术，特别将其应用于图像分类任务中以识别图像的关键区域。