A bargaining set for roommate problems

Ata Atay, Ana Mauleon and Vincent Vannetelbosch

Journal of Mathematical Economics, 2021, vol. 94, issue C

Abstract: Since stable matchings may not exist, we propose a weaker notion of stability based on the credibility of blocking pairs. We adopt the weak stability notion of Klijn and Massó (2003) for the marriage problem and we extend it to the roommate problem. We first show that although stable matchings may not exist, a weakly stable matching always exists in a roommate problem. Then, we adopt a solution concept based on the credibility of the deviations for the roommate problem: the bargaining set. We show that weak stability is not sufficient for a matching to be in the bargaining set. We generalize the coincidence result for marriage problems of Klijn and Massó (2003) between the bargaining set and the set of weakly stable and weakly efficient matchings to roommate problems. Finally, we prove that the bargaining set for roommate problems is always non-empty by making use of the coincidence result.

Keywords: Roommate problem; Matching; (Weak) stability; Bargaining set (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Working Paper: A bargaining set for roommate problems (2021)
Working Paper: A bargaining set for roommate problems (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:94:y:2021:i:c:s0304406820301427

DOI: 10.1016/j.jmateco.2020.102465

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