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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

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    1. Hatfield, John William & Kojima, Fuhito, 2010. "Substitutes and stability for matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1704-1723, September.
    2. Ortega, Josué & Klein, Thilo, 2023. "The cost of strategy-proofness in school choice," Games and Economic Behavior, Elsevier, vol. 141(C), pages 515-528.
    3. Troyan, Peter & Delacrétaz, David & Kloosterman, Andrew, 2020. "Essentially stable matchings," Games and Economic Behavior, Elsevier, vol. 120(C), pages 370-390.
    4. Yusuke Iwase, 2022. "Equivalence theorem in matching with contracts," Review of Economic Design, Springer;Society for Economic Design, vol. 26(1), pages 117-125, March.
    5. 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.
    6. Josué Ortega & Erel Segal-Halevi, 2022. "Obvious manipulations in cake-cutting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 969-988, November.
    7. 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.
    8. Alva, Samson & Manjunath, Vikram, 2019. "Strategy-proof Pareto-improvement," Journal of Economic Theory, Elsevier, vol. 181(C), pages 121-142.
    9. Troyan, Peter & Morrill, Thayer, 2020. "Obvious manipulations," Journal of Economic Theory, Elsevier, vol. 185(C).
    10. 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.
    11. 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.
    12. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 1297-1348.
    13. Toyotaka Sakai, 2011. "A note on strategy-proofness from the doctor side in matching with contracts," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 337-342, December.
    14. Arribillaga, R. Pablo & Bonifacio, Agustín G., 2024. "Obvious manipulations of tops-only voting rules," Games and Economic Behavior, Elsevier, vol. 143(C), pages 12-24.
    15. 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.
    16. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    17. Hirata, Daisuke & Kasuya, Yusuke, 2017. "On stable and strategy-proof rules in matching markets with contracts," Journal of Economic Theory, Elsevier, vol. 168(C), pages 27-43.
    18. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the New York City High School Match," NBER Working Papers 14864, National Bureau of Economic Research, Inc.
    19. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
    20. Claudia Cerrone & Yoan Hermstrüwer & Onur Kesten, 2024. "School Choice with Consent: an Experiment," The Economic Journal, Royal Economic Society, vol. 134(661), pages 1760-1805.
    21. Philip J. Reny, 2022. "Efficient Matching in the School Choice Problem," American Economic Review, American Economic Association, vol. 112(6), pages 2025-2043, June.
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    Cited by:

    1. R. Pablo Arribillaga & Agustín G. Bonifacio, 2025. "Not obviously manipulable allotment rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 80(1), pages 355-380, August.
    2. Arribillaga, R. Pablo & Bonifacio, Agustín G., 2025. "Obvious manipulations, consistency, and the uniform rule," Economics Letters, Elsevier, vol. 252(C).
    3. Hiroki Shinozaki, 2025. "Non-obvious manipulability in package assignment problems with money," International Journal of Game Theory, Springer;Game Theory Society, vol. 54(2), pages 1-35, December.
    4. Hinata Kurashita & Ryosuke Sakai, 2025. "Egalitarian-equivalent and strategy-proof mechanisms in homogeneous multi-object allocation problems," Papers 2507.09152, arXiv.org.
    5. 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.

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    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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