Von Neumann-Morgenstern Stable Sets in Matching Problems

Lars Ehlers

Cahiers de recherche from Centre interuniversitaire de recherche en économie quantitative, CIREQ

Abstract: The 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.

Keywords: matching problem; Von Neumann-Morgenstern stable sets (search for similar items in EconPapers)
JEL-codes: C78 J41 J44 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2005
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Citations: View citations in EconPapers (4)

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Related works:
Journal Article: Von Neumann-Morgenstern stable sets in matching problems (2007)
Working Paper: Von Neumann-Morgenstern Stable Sets in Matching Problems (2005)
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Persistent link: https://EconPapers.repec.org/RePEc:mtl:montec:12-2005

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