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Obvious Manipulations in Matching with and without Contracts

Author

Listed:
  • Pablo R. Arribillaga

    (UNSL/CONICET)

  • Eliana Pepa Risma

    (UNSL/CONICET)

Abstract

In a many-to-one matching model, with or without contracts, where doctors’ preferences are private information and hospitals’ preferences are substitutable and public information, any stable matching rule could be manipulated for doctors. Since manipulations can not be completely avoided, we consider the concept of obvious manipulations and look for stable matching rules that prevent at least such manipulations (for doctors). For the model with contracts, we prove that: (i) the doctor-optimal matching rule is non-obviously manipulable and (ii) the hospital-optimal matching rule is obviously manipulable, even in the one-to-one model. In contrast to (ii), for a many-to-one model without contracts, we prove that the hospital-optimal matching rule is not obviously manipulable.Furthermore, if we focus on quantile stable rules, then we prove that the doctor-optimal matching rule is the only non-obviously manipulable quantile stable rule

Suggested Citation

  • Pablo R. Arribillaga & Eliana Pepa Risma, 2023. "Obvious Manipulations in Matching with and without Contracts," Working Papers 257, Red Nacional de Investigadores en Economía (RedNIE).
    • Handle: RePEc:aoz:wpaper:257
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    File URL: https://rednie.eco.unc.edu.ar/files/DT/257.pdf
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    References listed on IDEAS

    as
    1. Troyan, Peter & Morrill, Thayer, 2020. "Obvious manipulations," Journal of Economic Theory, Elsevier, vol. 185(C).
    2. Ruth Martínez & Jordi Massó & Alejdanro Neme & Jorge Oviedo, 2004. "On group strategy-proof mechanisms for a many-to-one matching model," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 115-128, January.
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    4. Pepa Risma, Eliana, 2015. "Binary operations and lattice structure for a model of matching with contracts," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 6-12.
    5. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    6. Troyan, Peter & Delacrétaz, David & Kloosterman, Andrew, 2020. "Essentially stable matchings," Games and Economic Behavior, Elsevier, vol. 120(C), pages 370-390.
    7. 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.
    8. Fernandez, Marcelo Ariel, 2018. "Deferred acceptance and regret-free truth-telling," Economics Working Paper Archive 65832, The Johns Hopkins University,Department of Economics, revised 31 Jul 2020.
    9. 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. SHINOZAKI, Hiroki, 2023. "Non-obvious manipulability and efficiency in package assignment problems with money for agents with income effects and hard budget constraints," Discussion paper series HIAS-E-136, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    2. R. Pablo Arribillaga & Agustin G. Bonifacio, 2023. "Not obviously manipulable allotment rules," Papers 2309.06546, arXiv.org, revised Apr 2024.

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    More about this item

    Keywords

    obvious manipulations; matching; contracts;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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