论文标题
关于琐事的无嫉妒分配
On the Envy-free Allocation of Chores
论文作者
论文摘要
我们研究了将一组不可分割的家务分配给三种代理的问题，其中两个具有添加成本功能，以公平的方式。正在考虑的两个公平的概念是嫉妒的，直到任何琐事（EFX）和一个放松的概念，即转移任何琐事（TEFX）的嫉妒。与货物相反，琐事的情况仍然相对尚未探索。特别是，如果其中两个具有附加成本功能，并且其最高和最低成本的比率是两个界限，那么我们的结果可以建设性地证明了三种代理的TEFX分配。此外，如果这两个成本函数在杂务成本上具有相同的排序（IDO），那么即使对比率结合的条件略有放松，也存在EFX分配。在我们的整个框架中，除了具有单调成本函数外，第三代理都不受限制。
We study the problem of allocating a set of indivisible chores to three agents, among whom two have additive cost functions, in a fair manner. Two fairness notions under consideration are envy-freeness up to any chore (EFX) and a relaxed notion, namely envy-freeness up to transferring any chore (tEFX). In contrast to the case of goods, the case of chores remain relatively unexplored. In particular, our results constructively prove the existence of a tEFX allocation for three agents if two of them have additive cost functions and the ratio of their highest and lowest costs is bounded by two. In addition, if those two cost functions have identical ordering (IDO) on the costs of chores, then an EFX allocation exists even if the condition on the ratio bound is slightly relaxed. Throughout our entire framework, the third agent is unrestricted besides having a monotone cost function.
