lynx   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/aoz/wpaper/363.html
   My bibliography  Save this paper

Obvious Manipulations, Stability, and Efficiency in Matching Markets with No, Unitary, and Multiple Contracts: Three Different Results

Author

Listed:
  • R. Pablo Arribillaga

    (CONICET/UNSL)

  • Beatriz Millan

    (CONICET/UNSL/UNSJ)

  • Eliana Pepa Risma

    (CONICET/UNSL)

Abstract
In two-sided many-to-many matching markets under substitutable preferences —both with and without contracts— all stable-dominating mechanisms are manipulable. In light of this, we examine whether some of these mechanisms are at least not obviously manipulable (NOM). To this end, we discuss three established models that are encompassed by our general framework: the no-contract case, the unitary con tract case, and the multiple-contract case. Our results reveal fundamental differences among the three models. We transition from a no-contracts model, where all stable dominating mechanisms are NOM, to a multiple-contracts model, where all stable mechanisms and all efficient stable-dominating mechanisms are obviously manipulable (OM). In the intermediate case of unitary contracts the doctor-proposing DA mechanism remains NOM, but the hospital-proposing DA mechanism and all efficient stable-dominating mechanisms are OM. These findings reveal fundamental trade-offs between stability, efficiency, and NOM in these markets.

Suggested Citation

  • R. Pablo Arribillaga & Beatriz Millan & Eliana Pepa Risma, 2025. "Obvious Manipulations, Stability, and Efficiency in Matching Markets with No, Unitary, and Multiple Contracts: Three Different Results," Working Papers 363, Red Nacional de Investigadores en Economía (RedNIE).
    • Handle: RePEc:aoz:wpaper:363
    as

    Download full text from publisher

    File URL: https://rednie.eco.unc.edu.ar/files/DT/363.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dogan, Battal & Ehlers, Lars, 2021. "Minimally unstable Pareto improvements over deferred acceptance," Theoretical Economics, Econometric Society, vol. 16(4), November.
    2. Klaus, Bettina & Walzl, Markus, 2009. "Stable many-to-many matchings with contracts," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 422-434, July.
    3. 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.
    4. Troyan, Peter & Delacrétaz, David & Kloosterman, Andrew, 2020. "Essentially stable matchings," Games and Economic Behavior, Elsevier, vol. 120(C), pages 370-390.
    5. 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.
    6. Kominers, Scott Duke, 2012. "On the correspondence of contracts to salaries in (many-to-many) matching," Games and Economic Behavior, Elsevier, vol. 75(2), pages 984-989.
    7. Yuichiro Kamada & Fuhito Kojima, 2024. "Fair Matching under Constraints: Theory and Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(2), pages 1162-1199.
    8. , & ,, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    9. Alva, Samson & Manjunath, Vikram, 2019. "Strategy-proof Pareto-improvement," Journal of Economic Theory, Elsevier, vol. 181(C), pages 121-142.
    10. Hatfield, John William & Kominers, Scott Duke, 2017. "Contract design and stability in many-to-many matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 78-97.
    11. Agustín Bonifacio & Noelia Juarez & Paola Manasero, 2024. "Lattice Operations for the Stable Set in Substitutable Matching Markets via re-equilibration Dynamics," Working Papers 333, Red Nacional de Investigadores en Economía (RedNIE).
    12. Troyan, Peter & Morrill, Thayer, 2020. "Obvious manipulations," Journal of Economic Theory, Elsevier, vol. 185(C).
    13. 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.
    14. 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.
    15. 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.
    16. Federico Echenique, 2012. "Contracts versus Salaries in Matching," American Economic Review, American Economic Association, vol. 102(1), pages 594-601, February.
    17. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 1297-1348.
    18. 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.
    19. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    20. Sotomayor, Marilda, 1996. "A Non-constructive Elementary Proof of the Existence of Stable Marriages," Games and Economic Behavior, Elsevier, vol. 13(1), pages 135-137, March.
    21. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arribillaga, R. Pablo & Pepa Risma, Eliana, 2025. "Obvious manipulations in matching with and without contracts," Games and Economic Behavior, Elsevier, vol. 151(C), pages 70-81.
    2. Somouaoga Bonkoungou, 2021. "Decentralized college admissions under single application," Review of Economic Design, Springer;Society for Economic Design, vol. 25(1), pages 65-91, June.
    3. Rodríguez-Álvarez, Carmelo & Romero-Medina, Antonio, 2024. "School choice with transferable student characteristics," Games and Economic Behavior, Elsevier, vol. 143(C), pages 103-124.
    4. Antonio Romero-Medina & Matteo Triossi, 2023. "Take-it-or-leave-it contracts in many-to-many matching markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(2), pages 591-623, February.
    5. Klijn, Flip & Yazıcı, Ayşe, 2014. "A many-to-many ‘rural hospital theorem’," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 63-73.
    6. Jonathan Ma & Scott Duke Kominers, 2018. "Bundling Incentives in (Many-to-Many) Matching with Contracts," Harvard Business School Working Papers 19-011, Harvard Business School.
    7. 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.
    8. Zhang, Jun, 2023. "Strategy-proof allocation with outside option," Games and Economic Behavior, Elsevier, vol. 137(C), pages 50-67.
    9. Hatfield, John William & Kominers, Scott Duke, 2015. "Multilateral matching," Journal of Economic Theory, Elsevier, vol. 156(C), pages 175-206.
    10. Chao Huang, 2021. "Stable matching: an integer programming approach," Papers 2103.03418, arXiv.org, revised Apr 2022.
    11. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    12. Umut M. Dur & Scott Duke Kominers & Parag A. Pathak & Tayfun Sönmez, 2013. "The Demise of Walk Zones in Boston: Priorities vs. Precedence in School Choice," NBER Working Papers 18981, National Bureau of Economic Research, Inc.
    13. Troyan, Peter & Delacrétaz, David & Kloosterman, Andrew, 2020. "Essentially stable matchings," Games and Economic Behavior, Elsevier, vol. 120(C), pages 370-390.
    14. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 537-569, March.
    15. Minoru Kitahara & Yasunori Okumura, 2021. "Improving efficiency in school choice under partial priorities," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 971-987, December.
    16. Hatfield, John William & Kominers, Scott Duke, 2017. "Contract design and stability in many-to-many matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 78-97.
    17. Mustafa Oğuz Afacan & Umut Dur, 2023. "Strategy‐proof size improvement: is it possible?," Scandinavian Journal of Economics, Wiley Blackwell, vol. 125(2), pages 321-338, April.
    18. Tayfun Sönmez & Tobias B. Switzer, 2013. "Matching With (Branch‐of‐Choice) Contracts at the United States Military Academy," Econometrica, Econometric Society, vol. 81(2), pages 451-488, March.
    19. Alcalde, José, 2018. "Beyond the Spanish MIR with consent: (Hidden) cooperation and coordination in matching," Games and Economic Behavior, Elsevier, vol. 110(C), pages 32-49.
    20. Agustin G. Bonifacio & Nadia Guiñazú & Noelia Juarez & Pablo Neme & Jorge Oviedo, 2024. "The lattice of envy-free many-to-many matchings with contracts," Theory and Decision, Springer, vol. 96(1), pages 113-134, February.

    More about this item

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aoz:wpaper:363. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Laura Inés D Amato (email available below). General contact details of provider: https://edirc.repec.org/data/redniar.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.
    Лучший частный хостинг