Von Neumann-Morgenstern Stable Sets in Matching Problems
AbstractThe following properties of the core of a one-to-one matching problem are 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 problems. We show that a set of matchings is a stable set of a 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; and (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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Bibliographic InfoPaper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 12-2005.
Length: 30 pages
Date of creation: 2005
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matching problem; Von Neumann-Morgenstern stable sets;
Other versions of this item:
- Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
- EHLERS, Lars, 2005. "Von Neumann-Morgenstern Stable Sets in Matching Problems," Cahiers de recherche 2005-11, Universite de Montreal, Departement de sciences economiques.
- C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
- J41 - Labor and Demographic Economics - - Particular Labor Markets - - - Labor Contracts
- J44 - Labor and Demographic Economics - - Particular Labor Markets - - - Professional Labor Markets and Occupations
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