# A bargaining set for roommate problems

Working paper

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.