Weak Stability and a Bargaining Set for the Marriage Model

F. Klijn, J. Masso

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Abstract

In this note we introduceweak 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 themembers 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) for this context.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages11
Volume1999-114
Publication statusPublished - 1999

Publication series

NameCentER Discussion Paper
Volume1999-114

Fingerprint

Bargaining set
Marriage
Threat

Keywords

  • matching
  • (weak) stability
  • bargaining set

Cite this

Klijn, F., & Masso, J. (1999). Weak Stability and a Bargaining Set for the Marriage Model. (CentER Discussion Paper; Vol. 1999-114). Tilburg: Operations research.
Klijn, F. ; Masso, J. / Weak Stability and a Bargaining Set for the Marriage Model. Tilburg : Operations research, 1999. (CentER Discussion Paper).
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Klijn, F & Masso, J 1999 'Weak Stability and a Bargaining Set for the Marriage Model' CentER Discussion Paper, vol. 1999-114, Operations research, Tilburg.

Weak Stability and a Bargaining Set for the Marriage Model. / Klijn, F.; Masso, J.

Tilburg : Operations research, 1999. (CentER Discussion Paper; Vol. 1999-114).

Research output: Working paperDiscussion paperOther research output

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AU - Masso, J.

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N2 - In this note we introduceweak 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 themembers 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) for this context.

AB - In this note we introduceweak 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 themembers 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) for this context.

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Klijn F, Masso J. Weak Stability and a Bargaining Set for the Marriage Model. Tilburg: Operations research. 1999. (CentER Discussion Paper).