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

Author

Listed:
  • 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.

Suggested Citation

  • 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.
    • 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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    Citations

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    Cited by:

    1. 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.
    2. Yuichiro Kamada & Fuhito Kojima, 2020. "Accommodating various policy goals in matching with constraints," The Japanese Economic Review, Springer, vol. 71(1), pages 101-133, January.
    3. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October.
    4. Rêgo, Leandro Chaves & Kilgour, D. Marc, 2022. "Choice stabilities in the graph model for conflict resolution," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1064-1071.
    5. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
    6. Paula Jaramillo & Çaǧatay Kayı & Flip Klijn, 2014. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 793-811, April.
    7. Cantala, David, 2004. "Restabilizing matching markets at senior level," Games and Economic Behavior, Elsevier, vol. 48(1), pages 1-17, July.
    8. Kadam, Sangram V. & Kotowski, Maciej H., 2018. "Time horizons, lattice structures, and welfare in multi-period matching markets," Games and Economic Behavior, Elsevier, vol. 112(C), pages 1-20.
    9. Tsuyoshi Adachi & Yuki Ishibashi, 2022. "Stability and strategy-proofness for matching with interval constraints," Working Papers 2124, Waseda University, Faculty of Political Science and Economics.
    10. David Cantala, 2011. "Agreement toward stability in matching markets," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 293-316, December.
    11. 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.
    12. Klijn, Flip & Yazıcı, Ayşe, 2014. "A many-to-many ‘rural hospital theorem’," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 63-73.
    13. 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.
    14. , & ,, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    15. Kamada, Yuichiro & Kojima, Fuhito, 2018. "Stability and strategy-proofness for matching with constraints: a necessary and sufficient condition," Theoretical Economics, Econometric Society, vol. 13(2), May.
    16. Jiao, Zhenhua & Tian, Guoqiang & Chen, Songqing & Yang, Fei, 2016. "The blocking lemma and group incentive compatibility for matching with contracts," Mathematical Social Sciences, Elsevier, vol. 82(C), pages 65-71.
    17. Chambers, Christopher P. & Yenmez, M. Bumin, 2018. "On lexicographic choice," Economics Letters, Elsevier, vol. 171(C), pages 222-224.
    18. Kumano, Taro & Watabe, Masahiro, 2012. "Dominant strategy implementation of stable rules," Games and Economic Behavior, Elsevier, vol. 75(1), pages 428-434.
    19. Yang, Yi-You, 2020. "Rationalizable choice functions," Games and Economic Behavior, Elsevier, vol. 123(C), pages 120-126.
    20. Kumano, Taro & Watabe, Masahiro, 2011. "Untruthful dominant strategies for the deferred acceptance algorithm," Economics Letters, Elsevier, vol. 112(2), pages 135-137, August.
    21. Mehmet Ekmekci & M. Bumin Yenmez, "undated". "Integrating Schools for Centralized Admissions," GSIA Working Papers 2014-E20, Carnegie Mellon University, Tepper School of Business.
    22. Ekmekci, Mehmet & Yenmez, M. Bumin, 2019. "Common enrollment in school choice," Theoretical Economics, Econometric Society, vol. 14(4), November.
    23. David Cantala, 2002. "Agreement toward stability in senior matching markets," Department of Economics and Finance Working Papers EC200201, Universidad de Guanajuato, Department of Economics and Finance, revised Jun 2007.
    24. Battal Doğan & Kemal Yildiz, 2023. "Choice with Affirmative Action," Management Science, INFORMS, vol. 69(4), pages 2284-2296, April.
    25. Jiao, Zhenhua & Tian, Guoqiang, 2017. "The Blocking Lemma and strategy-proofness in many-to-many matchings," Games and Economic Behavior, Elsevier, vol. 102(C), pages 44-55.

    More about this item

    Keywords

    Stable matchings; revealed preference; choice function; lattice;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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