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Von Neumann-Morgenstern Stable Sets in Matching Problems

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  • EHLERS, Lars

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.

Suggested Citation

  • EHLERS, Lars, 2005. "Von Neumann-Morgenstern Stable Sets in Matching Problems," Cahiers de recherche 12-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    • Handle: RePEc:mtl:montec:12-2005
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    References listed on IDEAS

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    More about this item

    Keywords

    matching problem; Von Neumann-Morgenstern stable sets;

    JEL classification:

    • 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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