Abstract
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 location. We assume that number of rooms are limited and thus no student can live by himself. Each student has strict preferences over their roommates. Central notion in this problem is stability. We consider exchange-stability of Alcalde (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 on which exchange-stable matching is guaranteed to exist. We define more general domains of preferences on which exchange-stable matching is guaranteed to exist.
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