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 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.
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Notes
Usually students are desperate to get a dormitory room. Therefore, we assume that students prefer to live with anyone rather than not being able to get a room.
We contacted dormitories in some major universities in Turkey, which grant this opportunity to students.
Since no student can stay by himself, we do not consider his preferences over himself.
Banerjee et al. (2001) defined “top-coalition property” of preferences for coalition formation games which reduces to the \(\alpha \)-reducible preferences in roommate problems.
Although it is weaker (by definition) than \(\alpha \)-reducible, we still prefer to use different terminology than the one used in Alcalde (1995).
In a way k is the maximal size of a group of students in which any pair agree in preferences.
Note that in Example 2, set of students is split into two groups, where students in each group agree in preferences.
References
Aziz H, Goldwaser A (2017) Coalitional exchange stable matchings in marriage and roommate markets. In: AAMAS
Alcalde J (1995) Exchance-proofness or divorce-proofness? Stability in one-sided matching markets. Econ Des 1:275–287
Banerjee S, Konishi H, Sönmez T (2001) Core in simple coalition formation game. Soc Choice Welf 18:135–153
Cechlarova K (2002) On the complexity of exchange-stable roommates. Discrete Appl Math 116:279–287
Cechlarova K, Manlove DF (2005) The exchange-stable marriage problem. Discrete Appl Math 152:109–122
Chung K-S (2000) On the existence of stable roommate matchings. Games Econ Behav 36:206–230
Gale D, Shapley L (1962) College admissions and the stability of marriage. Am Math Mon 69:9–15
Gudmundsson J (2014) When do stable roommate matchings exist? A review. Rev Econ Des 18:151–161
Irving W (1985) An efficient algorithm for the stable roommates problem. J Algorithms 6:577–595
Morrill T (2010) The roommates problem revisited. J Econ Theory 145:1739–1756
Tan JJM (1991) A necessary and sufficient condition for the existence of a complete stable matching. J Algorithms 12:154–178
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I would like to thank Mustafa Oǧuz Afacan, Umut Dur, Lars Ehlers, Farhad Husseinov, Kerim Keskin, Thayer Morrill, Bumin Yenmez and participants of GAMES2016 and 13th Meeting of Society for Social Choice and Welfare for their insightful comments.
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Abizada, A. Exchange-stability in roommate problems. Rev Econ Design 23, 3–12 (2019). https://doi.org/10.1007/s10058-018-0217-0
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DOI: https://doi.org/10.1007/s10058-018-0217-0