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Two-sided matching with one-sided preferences

Author

Listed:
  • Guillaume Haeringer

    (Zicklin School of Business - Baruch College [CUNY] - CUNY - City University of New York [New York])

  • Vincent Iehlé

    (LEDa - Laboratoire d'Economie de Dauphine - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

In a school choice context we show that considering only schools' priorities and the set of acceptable schools for each student - but not how these schools are ranked in their preferences - we can restrict the set of possible stable matchings that can arise for any preference profile of the students that leaves the set of acceptable schools unchanged. We characterize impossible matches, i.e., of pairs student school that cannot be matched at any stable matching, for any preference profile. Our approach consists of linking Hall's marriage condition to stable matchings. Our results offer a new methodology to assess to what extent the preferences on one side of a matching market can preset the stable matchings that can emerge. First, we use this technique to discuss the impact of priority zoning in school choice problems. Second, a new mechanism for school choice problems is proposed. It is shown that it (weakly) Pareto dominates the Student Optimal Stable Mechanism and retain some of its incentives.

Suggested Citation

  • Guillaume Haeringer & Vincent Iehlé, 2014. "Two-sided matching with one-sided preferences," Working Papers halshs-00980794, HAL.
    • Handle: RePEc:hal:wpaper:halshs-00980794
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00980794
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    References listed on IDEAS

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    1. Caterina Calsamiglia & Guillaume Haeringer & Flip Klijn, 2010. "Constrained School Choice: An Experimental Study," American Economic Review, American Economic Association, vol. 100(4), pages 1860-1874, September.
    2. Martínez, Ruth & Massó, Jordi & Neme, Alejandro & Oviedo, Jorge, 2012. "On the invariance of the set of Core matchings with respect to preference profiles," Games and Economic Behavior, Elsevier, vol. 74(2), pages 588-600.
    3. Parag A. Pathak & Alvin E. Roth, 2013. "Matching with Couples: Stability and Incentives in Large Markets," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(4), pages 1585-1632.
    4. Federico Echenique & Sangmok Lee & Matthew Shum & M. Bumin Yenmez, 2013. "The Revealed Preference Theory of Stable and Extremal Stable Matchings," Econometrica, Econometric Society, vol. 81(1), pages 153-171, January.
    5. Roth, Alvin E, 1986. "On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets," Econometrica, Econometric Society, vol. 54(2), pages 425-427, March.
    6. Parag A. Pathak & Tayfun Sönmez, 2013. "School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation," American Economic Review, American Economic Association, vol. 103(1), pages 80-106, February.
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    14. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, vol. 99(5), pages 1954-1978, December.
    15. Scott Duke Kominers & Tayfun Sönmez, 2012. "Designing for Diversity: Matching with Slot-Specific Priorities," Boston College Working Papers in Economics 806, Boston College Department of Economics.
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    Cited by:

    1. Ahamad, Mazbahul, 2016. "Envious Preferences in Two-sided Matching," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 235482, Agricultural and Applied Economics Association.
    2. Daniela Saban & Jay Sethuraman, 2015. "The Complexity of Computing the Random Priority Allocation Matrix," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 1005-1014, October.

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    Keywords

    school Choice; Hall's marriage theorem; stable matching; zoning policy; Pareto improvement;
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