This paper extends the roommate problem to include externalities, allowing preferences for a partner to depend on the situation of others. Stability concepts for matchings and partitions of the set of agents are proposed and characterized, conditional on all agents having prudent expectations about other agents’ reactions to deviations. We prove that any roommate problem with externalities has a stable partition and that a stable matching exists if there is a stable partition without odd rings. These results allow us to find restrictions on the space of preferences ensuring the existence of a stable matching. We also show that some classical properties are lost in the presence of externalities: the existence of paths to stability from any unstable matching, the coincidence of the core with the set of stable matchings, and the invariance of the set of agents who are alone in a stable matching.

本文将室友问题扩展到包括外部性，允许伙伴的偏好取决于他人的情况。提出并表征了一组代理的匹配和划分的稳定性概念，其条件是所有代理对其他代理对偏差的反应具有谨慎的期望。我们证明，任何具有外部性的室友问题都具有稳定的分区，并且如果存在没有奇数环的稳定分区，则存在稳定的匹配。这些结果使我们能够找到对偏好空间的限制，以确保稳定匹配的存在。我们还表明，在存在外部性的情况下，一些经典属性会丢失：存在从任何不稳定匹配到稳定性的路径，核心与一组稳定匹配的重合，