你的大学宿舍与室友：带外部性的公平资源共享
Your College Dorm and Dormmates: Fair Resource Sharing with Externalities
AI总结：
本文研究带同伴外部性的公平资源共享与宿舍分配，刻画强无嫉妒的判定困难，证明容量2时Pareto无嫉妒分配总存在并给出多项式算法，而容量3时无法保证。
摘要：
我们研究一个公平资源共享问题，其中一组资源将在一群智能体之间共享。每个智能体需求一种资源，而每种资源只能服务有限数量的智能体。智能体不仅关心自己获得哪种资源，也关心由与其共享同一资源的伙伴所带来的外部性。显然，强无嫉妒这一概念——即没有智能体嫉妒他人的资源或伙伴——并不总能实现；我们证明，即使只是判断这种强无嫉妒分配是否存在，也是一个难以处理的问题。因此，一个更有意思的问题是，一种放宽的无嫉妒概念，即 Pareto 无嫉妒性，是否以及在何种情形下能够实现。在这一放宽概念下，一个智能体只有在同时嫉妒另一个智能体的资源和伙伴时，才会嫉妒该智能体。我们特别关注宿舍分配问题：学生需要被分配到容量相同的宿舍，并且他们对室友具有二分偏好。我们证明，当每间宿舍容量为 2 时，Pareto 无嫉妒分配总是存在，并提出一种多项式时间算法来计算这种分配。然而，当容量增加到 3 时，该结论立即失效；在这种情况下，即使 Pareto 无嫉妒性也无法保证。除存在性结果外，我们还研究了模型中（Pareto）无嫉妒分配的效用保证。
英文摘要：
We study a fair resource sharing problem, where a set of resources are to be shared among a group of agents. Each agent demands one resource and each resource can serve a limited number of agents. An agent cares about what resource they get as well as the externalities imposed by their mates, who share the same resource with them. Clearly, the strong notion of envy-freeness, where no agent envies another for their resource or mates, cannot always be achieved and we show that even deciding the existence of such a strongly envy-free assignment is an intractable problem. Hence, a more interesting question is whether (and in what situations) a relaxed notion of envy-freeness, the Pareto envy-freeness, can be achieved. Under this relaxed notion, an agent envies another only when they envy both the resource and the mates of the other agent. In particular, we are interested in a dorm assignment problem, where students are to be assigned to dorms with the same capacity and they have dichotomous preference over their dormmates. We show that when the capacity of each dorm is 2, a Pareto envy-free assignment always exists and we present a polynomial-time algorithm to compute such an assignment. Nevertheless, the result breaks immediately when the capacity increases to 3, in which case even Pareto envy-freeness cannot be guaranteed. In addition to the existential results, we also investigate the utility guarantees of (Pareto) envy-free assignments in our model.
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。
