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On the Invariance of the Set of Core Matchings with Respect to Preference Profiles

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We consider the general many-to-one matching model with ordinal preferences and give a procedure to partition the set of preference profiles into subsets with the property that all preference profiles in the same subset have the same Core. We also show how to identify a profile of (incomplete) binary relations containing the minimal information needed to generate as strict extensions all the (complete) preference profiles with the same Core. This is important for applications since it reduces the amount of information that agents have to reveal about their preference relations to centralized Core matching mechanisms; moreover, this reduction is maximal.

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  • Ruth Martínez & Jordi Massó & Alejandro Neme & Jorge Oviedo, 2009. "On the Invariance of the Set of Core Matchings with Respect to Preference Profiles," UFAE and IAE Working Papers 803.09, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    • Handle: RePEc:aub:autbar:803.09
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    References listed on IDEAS

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    1. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882.
    2. Ruth Martínez & Jordi Massó & Alejandro Neme & Jorge Oviedo, 2008. "On the invariance of the set of stable matchings with respect to substitutable preference profiles," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 497-518, March.
    3. Paul Milgrom, 2009. "Assignment Messages and Exchanges," American Economic Journal: Microeconomics, American Economic Association, vol. 1(2), pages 95-113, August.
    4. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    5. Charles Blair, 1988. "The Lattice Structure of the Set of Stable Matchings with Multiple Partners," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 619-628, November.
    6. Federico Echenique, 2008. "What Matchings Can Be Stable? The Testable Implications of Matching Theory," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 757-768, August.
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    Cited by:

    1. Guillaume Haeringer & Vincent Iehlé, 2019. "Two-Sided Matching with (Almost) One-Sided Preferences," American Economic Journal: Microeconomics, American Economic Association, vol. 11(3), pages 155-190, August.
    2. Schlegel, Jan Christoph, 2015. "Contracts versus salaries in matching: A general result," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 552-573.
    3. Jan Christoph Schlegel, 2014. "Contracts versus Salaries in Matching: A General Result. N.B.: This paper replaces Nr 13.09 "Contracts versus Salaries in Matching: Comment", (June 2013)," Cahiers de Recherches Economiques du Département d'économie 14.05, Université de Lausanne, Faculté des HEC, Département d’économie.
    4. Guillaume Haeringer & Vincent Iehlé, 2014. "Two-sided matching with one-sided preferences," Working Papers halshs-00980794, HAL.
    5. Alva, Samson, 2018. "WARP and combinatorial choice," Journal of Economic Theory, Elsevier, vol. 173(C), pages 320-333.
    6. Guillaume Haeringer & Vincent Iehlé, 2019. "Two-Sided Matching with (Almost) One-Sided Preferences," American Economic Journal: Microeconomics, American Economic Association, vol. 11(3), pages 155-190, August.

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    More about this item

    Keywords

    Matching; Core;

    JEL classification:

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

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