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A bargaining set for roommate problems

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Working paper
Author/s: 
Ata Atay, Ana Mauleon and Vincent Vannetelbosch
Issue number: 
2019/12
Series: 
CORE Discussion Papers
Publisher: 
Université Catholique de Louvain
Year: 
2019
Since stable matchings may not exist, we adopt a weaker notion of stability for solving the roommate problem: the bargaining set. Klijn and MassÛ (2003) show that the bargaining set coincides with the set of weakly stable and weakly e¢ cient matchings in the marriage problem. First, we show that a weakly stable matching always exists in the roommate problem. However, weak stability is not su¢ cient for a matching to be in the bargaining set. Second, we prove that the bargaining set is always non-empty. Finally, as Klijn and MassÛ (2003) get for the marriage problem, we show that the bargaining set coincides with the set of weakly stable and weakly e¢ cient matchings in the roommate problem.
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