We study individually rational rules to be used to allot, among a group of agents, a perfectly divisible good that is freely available only in whole units. A rule is individually rational if, at each preference profile, each agent finds that her allotment is at least as good as any whole unit of the good. We study and characterize two individually rational and efficient families of rules, whenever agents' preferences are symmetric single‐peaked on the set of possible allotments. Rules in the two families are in addition envy‐free, but they differ on whether envy‐freeness is considered on losses or on awards. Our main result states that (a) the family of constrained equal losses rules coincides with the class of all individually rational and efficient rules that satisfy justified envy‐freeness on losses and (b) the family of constrained equal awards rules coincides with the class of all individually rational and efficient rules that satisfy envy‐freeness on awards.

中文翻译：

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当要分配的单位数是内生的时，关于分配问题的个体理性规则

我们单独研究合理的规则，以在一组代理之间分配完全可分割的商品，该商品只能在整个单位中免费使用。如果在每个偏好配置文件中，每个代理发现自己的分配至少与商品的任何整个单位一样好，则规则是个人合理的。每当代理人的偏好在可能的分配集合上对称且单一地表达时，我们就会研究并刻画两个单独的合理且有效的规则族。这两个家族中的规则在其他方面都是羡慕的，但是在损失或裁定是否考虑嫉妒方面却有所不同。