Pairwise Maximin Share Allocations Need Not Exist

2026-09-05

AI Summary

研究了不可分割物品在具有严格正加性估值的代理人之间的公平分配问题，通过构造实例证明了两两最大最小份额分配（PMMS）不一定总是存在。

Abstract

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.

Problem

• Pairwise Maximin Share
• fair allocation
• indivisible goods
• positive additive valuations

Innovation

• Pairwise Maximin Share (PMMS)
• Indivisible Goods
• Additive Valuations