We study one-sided matching problem, also known as roommate problem, where a group of people need to be paired in order to be assigned to certain rooms. We assume that number of rooms are limited and thus no one can be by himself. Each student has strict preferences over their roommates. Central notion in this problem is stability. We consider exchange-stability of Alcalde (Econ Des 1:275–287, 1995), which is immune to group of students exchanging their rooms/roommates with each other. He shows that exchange-stable matching may not always exist and considers specific domains of preferences to guarantee existence of such matching. We define more general domains of preferences on which exchange-stable matching is guaranteed to exist.

中文翻译：

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室友问题中的交换稳定性

我们研究单面匹配问题，也称为室友问题，其中需要将一组人配对才能分配给某些房间。我们假设房间数量有限，因此没有人可以独自居住。每个学生对室友都有严格的偏爱。这个问题的中心概念是稳定性。我们考虑了Alcalde的交换稳定性（Econ Des 1：275–287，1995），这不受一群学生互相交换房间/室友的影响。他表明交换稳定的匹配可能并不总是存在，并考虑了偏好的特定域以保证这种匹配的存在。我们定义了更普遍的偏好域，可以保证存在交换稳定匹配。