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Three-dimensional stable matching with cyclic preferences
Mälardalen University, Department of Mathematics and Physics.ORCID iD: 0000-0002-7164-0924
KTH.
Mälardalen University, Department of Mathematics and Physics.
2006 (English)In: Mathematical Social Sciences, ISSN 0165-4896, Vol. 52, no 1, 77-87 p.Article in journal (Refereed) Published
Abstract [en]

We consider stable three-dimensional matchings of three genders (3GSM). Alkan [Alkan, A., 1988. Non-existence of stable threesome matchings. Mathematical Social Sciences 16, 207–209] showed that not all instances of 3GSM allow stable matchings. Boros et al. [Boros, E., Gurvich, V., Jaslar, S., Krasner, D., 2004. Stable matchings in three-sided systems with cyclic preferences. Discrete Mathematics 286, 1–10] showed that if preferences are cyclic, and the number of agents is limited to three of each gender, then a stable matching always exists. Here we extend this result to four agents of each gender. We also show that a number of well-known sufficient conditions for stability do not apply to cyclic 3GSM. Based on computer search, we formulate a conjecture on stability of “strongest link” 3GSM, which would imply stability of cyclic 3GSM.

Place, publisher, year, edition, pages
2006. Vol. 52, no 1, 77-87 p.
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:mdh:diva-3433DOI: 10.1016/j.mathsocsci.2006.03.005ISI: 000239846900006Scopus ID: 2-s2.0-33746403368OAI: oai:DiVA.org:mdh-3433DiVA: diva2:116097
Available from: 2006-12-05 Created: 2006-12-05 Last updated: 2014-02-20Bibliographically approved

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