Stable matching of student-groups to dormitories

This paper generalizes results of former papers on the assignment of students to dormitories, under an entrance criterion, by allowing students to apply in groups. A group-application means that its applicants ask to be assigned to the same dormitory, and otherwise they prefer living off-campus. The underlying assumption in our model is that the dormitories share a common preference over the student-groups, which is given by a strictly increasing ranking of their credit scores. The definition of a quasi-stable outcome is adjusted in order to incorporate student-group applications, and we prove that such an outcome always exists. Furthermore, a polynomial-time algorithm that finds all the quasi-stable outcomes is proposed. Apparently, not all properties of the single students’ model continue to hold under group-applications. Finally, we consider the incentive compatibility property of the proposed algorithm, and describe a specific quasi-stable outcome for which no subset of student-groups can gain by misrepresenting their preferences over the dormitories.