Von Neumann-Morgenstern Stable Sets in Matching Problems
Article [Version of Record]
Is part of
Cahier de recherche ; no. 2005-11.Publisher(s)
Université de Montréal. Département de sciences économiques.Author(s)
Affiliation
Keywords
- Matching Problem
- Von Neumann-Morgenstern Stable Sets
- [JEL:C78] Mathematical and Quantitative Methods - Game Theory and Bargaining Theory - Bargaining Theory; Matching Theory
- [JEL:J41] Labor and Demographic Economics - Particular Labor Markets - Contracts: Specific Human Capital, Matching Models, Efficiency Wage Models, and Internal Labor Markets
- [JEL:J44] Labor and Demographic Economics - Particular Labor Markets - Professional Labor Markets and Occupations
- [JEL:C78] Mathématiques et méthodes quantitatives - Théorie des jeux et négociation - Théorie de la négociation et du "matching"
- [JEL:J41] Démographie et économie du travail - Marchés particuliers de travail - Contrats: capital humain spécifique, modèles de matching, modèles du salaire d'efficacité et marchés internes du travail
- [JEL:J44] Démographie et économie du travail - Marchés particuliers de travail - Marché du travail pour les professionnels
Abstract(s)
The following properties of the core of a one well-known: (i) the core is non-empty; (ii) the core is a lattice; and (iii) the set of unmatched agents is identical for any two matchings belonging to the core. The literature on two-sided matching focuses almost exclusively on the core and studies extensively its properties. Our main result is the following characterization of (von Neumann-Morgenstern) stable sets in one-to-one matching problem only if it is a maximal set satisfying the following properties : (a) the core is a subset of the set; (b) the set is a lattice; (c) the set of unmatched agents is identical for any two matchings belonging to the set. Furthermore, a set is a stable set if it is the unique maximal set satisfying properties (a), (b) and (c). We also show that our main result does not extend from one-to-one matching problems to many-to-one matching problems.
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