Weak stability and a bargaining set for the marriage model

In this note we introduce weak stability, a relaxation of the concept of stability for the marriage model by assuming that the agents are no longer myopic in choosing a blocking pair. The new concept is based on threats within blocking pairs: an individually rational matching is weakly stable if for every blocking pair one of the members can find a more attractive partner with whom he forms another blocking pair for the original matching. Our main result is that under the assumption of strict preferences, the set of weakly stable and weakly efficient matchings coincides with the bargaining set of Zhou (1994, Games Econ. Behav. 6, 512-526) for this context. © 2002 Elsevier Science (USA). All rights reserved.