在具有二值子模估值的智能体之间分配优质与更优质物品
Dividing Good and Better Items Among Agents with Bivalued Submodular Valuations
AI总结：
该研究针对二值子模估值下的不可分割物品公平分配问题，基于Yankee Swap机制提出序列算法框架，证明a整除b时可计算多种福利最大化分配，并给出相应的最大最小份额保证，同时发现此类分配不满足EF1性质。
摘要：
我们研究了在具有二值子模估值的智能体之间公平分配一组不可分割物品的问题——每件物品提供的边际收益为a或b（a<b），且物品的边际收益递减。这是两类被广泛研究的估值类——二值加性估值和二元子模估值的自然推广。我们基于最近提出的Yankee Swap（洋基交换）机制，提出了一个简单的序列算法框架，当a整除b时，该框架可经调整用于计算多种解概念，包括最大纳什福利（MNW）、leximin（字典最小）和p-均值福利最大化分配。这一结果与现有结论形成互补，即当a不整除b时，MNW和leximin分配存在计算难解性。我们证明，当a整除b时，MNW和leximin分配分别保证每个智能体至少获得其最大最小份额的2/5和a/(b+2a)。我们还表明，leximin和MNW分配都无法保证满足“移除一件物品即无嫉妒（EF1）”。这一结果出人意料，因为对于更简单的二值加性估值和二元子模估值类，已知MNW分配满足“移除任意一件物品即无嫉妒（EFX）”。
英文摘要：
We study the problem of fairly allocating a set of indivisible goods among agents with {\em bivalued submodular valuations} -- each good provides a marginal gain of either $a$ or $b$ ($a < b$) and goods have decreasing marginal gains. This is a natural generalization of two well-studied valuation classes -- bivalued additive valuations and binary submodular valuations. We present a simple sequential algorithmic framework, based on the recently introduced Yankee Swap mechanism, that can be adapted to compute a variety of solution concepts, including max Nash welfare (MNW), leximin and $p$-mean welfare maximizing allocations when $a$ divides $b$. This result is complemented by an existing result on the computational intractability of MNW and leximin allocations when $a$ does not divide $b$. We show that MNW and leximin allocations guarantee each agent at least $\frac25$ and $\frac{a}{b+2a}$ of their maximin share, respectively, when $a$ divides $b$. We also show that neither the leximin nor the MNW allocation is guaranteed to be envy free up to one good (EF1). This is surprising since for the simpler classes of bivalued additive valuations and binary submodular valuations, MNW allocations are known to be envy free up to any good (EFX).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
