We study the fair division of items to agents supposing that agents can form groups. We thus give natural generalizations of popular concepts such as envy-freeness and Pareto efficiency to groups of fixed sizes. Group envy-freeness requires that no group envies another group. Group Pareto efficiency requires that no group can be made better off without another group be made worse off. We study these new group properties from an axiomatic viewpoint. We thus propose new fairness taxonomies that generalize existing taxonomies. We further study near versions of these group properties as allocations for some of them may not exist. We finally give three prices of group fairness between group properties for three common social welfares (i.e. utilitarian, egalitarian, and Nash).

中文翻译：

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具有不可分割项的公平除法中的群体嫉妒自由度和群体帕累托效率

我们研究将物品公平地分配给代理，假设代理可以形成组。因此，我们将流行概念（例如无嫉妒和帕累托效率）的自然概括为固定大小的组。无群体嫉妒要求没有一个群体嫉妒另一个群体。群体帕累托效率要求在没有另一个群体变坏的情况下，任何群体都不能变好。我们从公理的角度研究这些新的群属性。因此，我们提出了新的公平分类法，可以概括现有分类法。我们进一步研究了这些组属性的近版本，因为其中一些属性的分配可能不存在。我们最终给出了三种常见社会福利（即功利主义、平等主义和纳什）的群体属性之间的群体公平的三个价格。