PMMS 分配对于 3 个具有可加估值的智能体可能不存在
PMMS Allocations Need Not Exist for 3 Agents with Additive Valuations
浏览论文内容
中文总结 AI 辅助
本文构造反例证明在3个智能体、9个不可分割商品且估值可加时，PMMS分配不存在，并给出近似比上界78/79。
中文摘要 AI 辅助
本文给出一个实例，证明在具有不可分割商品和可加估值的某些公平分配问题中，任何分配都无法满足两两最大最小份额（PMMS）性质。该实例仅需 $n=3$ 个智能体和 $m=9$ 个商品，并附有不存在 PMMS 分配的证明。另一个实例（通过计算机穷举枚举验证）表明，PMMS 无法在比率高于 $78/79 \approx 0.987$ 的范围内被近似。
英文摘要
This note gives an instance demonstrating that the pairwise maximin share (PMMS) property cannot be satisfied by any allocation in certain fair division problems with indivisible goods and additive valuations. The instance requires only $n=3$ agents and $m=9$ goods, and is accompanied by a proof that no PMMS allocation exists. A separate instance shows (certified by exhaustive enumeration with a computer) that PMMS cannot be approximated within a ratio above $78/79 \approx 0.987$.
