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Von Neumann-Morgenstern stable sets in matching problems

  • Ehlers, Lars

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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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 134 (2007)
Issue (Month): 1 (May)
Pages: 537-547

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Handle: RePEc:eee:jetheo:v:134:y:2007:i:1:p:537-547
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Ahmet Alkan, 2001. "original papers : On preferences over subsets and the lattice structure of stable matchings," Review of Economic Design, Springer;Society for Economic Design, vol. 6(1), pages 99-111.
  2. Biswas, Amit K. & Parthasarathy, T. & Ravindran, G., 2001. "Stability and Largeness of the Core," Games and Economic Behavior, Elsevier, vol. 34(2), pages 227-237, February.
  3. Einy, Ezra & Holzman, Ron & Monderer, Dov & Shitovitz, Benyamin, 1996. "Core and Stable Sets of Large Games Arising in Economics," Journal of Economic Theory, Elsevier, vol. 68(1), pages 200-211, January.
  4. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
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  13. Einy, Ezra & Holzman, Ron & Monderer, Dov & Shitovitz, Benyamin, 1997. "Core Equivalence Theorems for Infinite Convex Games," Journal of Economic Theory, Elsevier, vol. 76(1), pages 1-12, September.
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