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original papers : On preferences over subsets and the lattice structure of stable matchings

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Author Info

  • Ahmet Alkan

    ()
    (Sabanci University, Tuzla 81474 Istanbul, Turkey)

Abstract

This paper studies the structure of stable multipartner matchings in two-sided markets where choice functions are quotafilling in the sense that they satisfy the substitutability axiom and, in addition, fill a quota whenever possible. It is shown that (i) the set of stable matchings is a lattice under the common revealed preference orderings of all agents on the same side, (ii) the supremum (infimum) operation of the lattice for each side consists componentwise of the join (meet) operation in the revealed preference ordering of the agents on that side, and (iii) the lattice has the polarity, distributivity, complementariness and full-quota properties.

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Bibliographic Info

Article provided by Springer in its journal Review of Economic Design.

Volume (Year): 6 (2001)
Issue (Month): 1 ()
Pages: 99-111

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Handle: RePEc:spr:reecde:v:6:y:2001:i:1:p:99-111

Note: Received: 5 March 1999 / Accepted: 12 May 2000
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Web page: http://link.springer.de/link/service/journals/10058/index.htm

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Related research

Keywords: Stable matchings; revealed preference; choice function; lattice;

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Cited by:
  1. Martínez, Ruth & Massó, Jordi & Neme, Alejandro & Oviedo, Jorge, 2010. "The Blocking Lemma for a many-to-one matching model," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 937-949, September.
  2. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October.
  3. Cantala, David, 2004. "Restabilizing matching markets at senior level," Games and Economic Behavior, Elsevier, vol. 48(1), pages 1-17, July.
  4. Monjardet, Bernard, 2003. "The presence of lattice theory in discrete problems of mathematical social sciences. Why," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 103-144, October.
  5. Paula Jaramillo & Kagi Cagatay & Flip Klijn, 2012. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," DOCUMENTOS DE TRABAJO 009997, UNIVERSIDAD DEL ROSARIO.
  6. Kumano, Taro & Watabe, Masahiro, 2012. "Dominant strategy implementation of stable rules," Games and Economic Behavior, Elsevier, vol. 75(1), pages 428-434.
  7. Kumano, Taro & Watabe, Masahiro, 2011. "Untruthful dominant strategies for the deferred acceptance algorithm," Economics Letters, Elsevier, vol. 112(2), pages 135-137, August.
  8. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2004. "An algorithm to compute the full set of many-to-many stable matchings," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 187-210, March.

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