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Deferred acceptance is minimally manipulable

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  • Martin Van der Linden

    (Utah State University)

Abstract

This paper shows that the deferred acceptance mechanism (DA) cannot be improved upon in terms of manipulability without compromising stability. A conflict between manipulability and fairness is also identified. Stable mechanisms that minimize the set of individuals who match with their least preferred achievable mate are shown to be maximally manipulable among the stable mechanisms. These mechanisms are also more manipulable than DA. A similar conflict between fairness and manipulability is identified in the case of the median stable mechanisms.

Suggested Citation

  • Martin Van der Linden, 2019. "Deferred acceptance is minimally manipulable," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 609-645, June.
    • Handle: RePEc:spr:jogath:v:48:y:2019:i:2:d:10.1007_s00182-018-0649-3
    DOI: 10.1007/s00182-018-0649-3
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    References listed on IDEAS

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    1. Maus, Stefan & Peters, Hans & Storcken, Ton, 2007. "Anonymous voting and minimal manipulability," Journal of Economic Theory, Elsevier, vol. 135(1), pages 533-544, July.
    2. SangMok Lee, 2017. "Incentive Compatibility of Large Centralized Matching Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(1), pages 444-463.
    3. Barberà, Salvador & Gerber, Anke, 2017. "Sequential voting and agenda manipulation," Theoretical Economics, Econometric Society, vol. 12(1), January.
    4. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-627, June.
    5. Bettina Klaus & Flip Klijn, 2006. "Median Stable Matching for College Admissions," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 1-11, April.
    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.
    7. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    8. Amartya Sen, 1999. "The Possibility of Social Choice," American Economic Review, American Economic Association, vol. 89(3), pages 349-378, June.
    9. Peter Chen & Michael Egesdal & Marek Pycia & M. Bumin Yenmez, 2016. "Manipulability of Stable Mechanisms," American Economic Journal: Microeconomics, American Economic Association, vol. 8(2), pages 202-214, May.
    10. Jay Sethuraman & Chung-Piaw Teo & Liwen Qian, 2006. "Many-to-One Stable Matching: Geometry and Fairness," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 581-596, August.
    11. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    12. Federico Echenique & Alistair J. Wilson & Leeat Yariv, 2016. "Clearinghouses for two‐sided matching: An experimental study," Quantitative Economics, Econometric Society, vol. 7(2), pages 449-482, July.
    13. Arribillaga, R. Pablo & Massó, Jordi, 2016. "Comparing generalized median voter schemes according to their manipulability," Theoretical Economics, Econometric Society, vol. 11(2), May.
    14. Andersson, Tommy & Ehlers, Lars & Svensson, Lars-Gunnar, 2014. "Least manipulable Envy-free rules in economies with indivisibilities," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 43-49.
    15. Roth, Alvin E & Vande Vate, John H, 1991. "Incentives in Two-Sided Matching with Random Stable Mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 31-44, January.
    16. P'eter Bir'o & Avinatan Hassidim & Assaf Romm & Ran I. Shorrer & S'andor S'ov'ag'o, 2020. "The Large Core of College Admission Markets: Theory and Evidence," Papers 2010.08631, arXiv.org, revised Aug 2022.
    17. Coles, Peter & Shorrer, Ran, 2014. "Optimal truncation in matching markets," Games and Economic Behavior, Elsevier, vol. 87(C), pages 591-615.
    18. Chung-Piaw Teo & Jay Sethuraman, 1998. "The Geometry of Fractional Stable Matchings and Its Applications," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 874-891, November.
    19. repec:oup:restud:v:84:y::i:1:p:444-463. is not listed on IDEAS
    20. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
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    Cited by:

    1. Decerf, Benoit & Van der Linden, Martin, 2021. "Manipulability in school choice," Journal of Economic Theory, Elsevier, vol. 197(C).
    2. Greg Leo & Jian Lou & Martin Van der Linden & Yevgeniy Vorobeychik & Myrna Wooders, 2021. "Matching soulmates," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(5), pages 822-857, October.

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    More about this item

    Keywords

    Matching; Deferred acceptance; Manipulability; Stability; Fairness;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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