发表机构
UNSW Sydney（新南威尔士大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究不可分割物品的公平分配，针对正加性估值下成对最大最小份额（PMMS）分配的存在性，通过构造四智能体反例，证明其不一定存在。
AI 中文摘要
我们研究了在具有严格正加性估值的智能体之间不可分割物品的公平分配问题。成对最大最小份额公平性（PMMS）要求，对于每一对有序智能体，第一个智能体对自己所得捆绑物品的估值，至少不低于她通过将这两个智能体的合并捆绑物品重新划分为两部分后所能确保的最佳最坏情况份额。自该概念提出以来，对于正加性估值，PMMS分配是否总是存在一直是一个悬而未决的问题。我们否定了这一问题。我们构造了一个包含四个智能体且具有严格正加性估值的实例，该实例不存在完整的PMMS分配。
英文摘要
We study the fair allocation of indivisible goods among agents with strictly positive additive valuations. Pairwise maximin share fairness (PMMS) asks that, for every ordered pair of agents, the first agent value her own bundle at least as highly as the best worst-case share she could secure by repartitioning the two agents' combined bundles into two parts. Whether a PMMS allocation always exists for positive additive valuations has remained open since the notion was introduced. We resolve this question in the negative. We construct an instance with four agents and strictly positive additive valuations that admits no complete PMMS allocation.
