多公寓租金分配
Multi-Apartment Rent Division
AI总结：
本文将单套公寓的租金分配推广到多套公寓选择与房内房间、租金同时公平分配的问题，提出协商无嫉妒性并证明其解存在且可多项式时间优化，同时研究更强的普遍无嫉妒性。
摘要：
租金分配是一个已被充分研究的问题，即在一套公寓内的一组室友之间公平地分配房间并分摊租金。现有解决方案的一个缺点是，它们假定租房者是孤立地考虑各套公寓，而在现实中，租房者可以在多套公寓之间进行选择。本文将租金分配问题推广到多公寓场景，其目标既是在一组备选方案中公平地选择一套公寓，也要在所选公寓内公平地分配房间和租金。我们的主要贡献是对无嫉妒性的一种推广，称为协商无嫉妒性。我们证明了满足协商无嫉妒性的解保证存在，并且可以在多项式时间内对所有协商无嫉妒解进行优化。我们还定义了一个更强的公平性概念，称为普遍无嫉妒性，并研究了当价值随机抽取时它的存在性。
英文摘要：
Rent division is the well-studied problem of fairly assigning rooms and dividing rent among a set of roommates within a single apartment. A shortcoming of existing solutions is that renters are assumed to be considering apartments in isolation, whereas in reality, renters can choose among multiple apartments. In this paper, we generalize the rent division problem to the multi-apartment setting, where the goal is to both fairly choose an apartment among a set of alternatives and fairly assign rooms and rents within the chosen apartment. Our main contribution is a generalization of envy-freeness called negotiated envy-freeness. We show that a solution satisfying negotiated envy-freeness is guaranteed to exist and that it is possible to optimize over all negotiated envy-free solutions in polynomial time. We also define an even stronger fairness notion called universal envy-freeness and study its existence when values are drawn randomly.
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。
