带可选出售的公平分配
Fair Allocation with Optional Selling
浏览论文内容
中文总结 AI 辅助
本文针对主体对不可分商品有主观估值且商品可按市价出售的场景，适配公平性概念并证明了多主体下满足MMS、SEFX等的分配存在性及比例的最优性。
中文摘要 AI 辅助
我们考虑在以下场景中对不可分商品进行公平分配：主体对商品集合具有主观估值函数，此外商品可按给定市场价格出售。在该场景中，公平分配需完成三项决策：确定出售哪些商品、如何分配未出售的商品、如何分配出售商品所得的资金。我们将基于份额的公平性概念（如最大最小份额（MMS）、截断比例份额（TPS））以及基于比较的公平性概念（如EF1、EFX，我们将其适配为SEF1和SEFX）应用到该场景中。当每个主体的效用在商品和资金上均为可加时，我们证明了以下结果：对于两个主体，存在同时满足MMS和SEFX的分配；对于三个主体，存在无法让每个主体获得超过11/12-MMS的实例；对于任意数量的主体，存在2/3-MMS分配；还存在同时满足SEFX和n/(2n-1)-TPS的分配，且即使不要求SEFX，该比例也是最优的。
英文摘要
We consider fair allocation of indivisible goods in a setting in which agents have subjective valuation functions over the set of goods, and in addition, goods may be sold at given market prices. In this setting, a fair allocation involves {deciding which goods to sell, how to allocate the unsold goods, and how to divide the money received from the sold goods.} We adapt to this setting the definitions of share-based fairness notions, such as the maximin share (MMS) and the truncated proportional share (TPS), and comparison-based fairness notions such as EF1 and EFX (which we adapt to SEF1 and SEFX). We show the following results when the utility of each agent is additive both over goods and over money. With two agents, there are allocations that are simultaneously MMS and SEFX. With three agents, there are instances in which no allocation gives every agent more than $\frac{11}{12}$-MMS. With any number of agents, there are $\frac{2}{3}$-MMS allocations. There also are allocations that are simultaneously SEFX and $\frac{n}{2n-1}$-TPS. This latter ratio is best possible, even without the SEFX requirement.
