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：我们研究了不可分割联盟博弈中的收益分配问题，其中大联盟的取值为自然数。该数值代表一定数量的不可分割对象，例如议会席位、肾脏交换资源或对机器学习模型输出结果起关键作用的顶级特征。本文旨在提出一种公平分配这些对象的方法。为此，我们定义了不可分割夏普利值并研究其性质。通过三个案例研究展示了所提技术的应用，特别地，我们将其用于图像分类任务中识别图像的关键区域。