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Obvious Manipulations in Matching without and with Contracts

Author

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  • R. Pablo Arribillaga
  • E. Pepa Risma

Abstract

This paper explores many-to-one matching models, both with and without contracts, where doctors' preferences are private and hospitals' preferences are public and substitutable. It is known that any stable-dominating mechanism --which is either stable or individually rational and Pareto-dominates (from the doctors' perspective) a stable mechanism--, is susceptible to manipulation by doctors. Our study focuses on \textit{obvious manipulations} and identifies stable-dominating mechanisms that prevent them. Without contracts, we show that more efficient mechanisms are less likely to be obviously manipulable and that any stable-dominating mechanism is not obviously manipulable. However, with contracts, none of these results hold. While we demonstrate that the Doctor-Proposing Deferred Acceptance (DA) Mechanism remains not obviously manipulable, we show that the Hospital-Proposing DA Mechanism and any efficient mechanism that Pareto-dominates the Doctor-Proposing DA Mechanism become (very) obviously manipulable, in the model with contracts.

Suggested Citation

  • R. Pablo Arribillaga & E. Pepa Risma, 2023. "Obvious Manipulations in Matching without and with Contracts," Papers 2306.17773, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2306.17773
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    5. 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. 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. 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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