IDEAS home Printed from https://ideas.repec.org/p/mtl/montec/04-2009.html
   My bibliography  Save this paper

Manipulation via Capacities Revisited

Author

Listed:
  • EHLERS, Lars

Abstract

This paper revisits manipulation via capacities in centralized two-sided matching markets. Sönmez (1997) showed that no stable mechanism is nonmanipulable via capacities. We show that non-manipulability via capacities can be equivalently described by two types of non-manipulation via capacities: non-Type-I-manipulability meaning that no college with vacant positions can manipulate by dropping some of its empty positions; and non-Type-II manipulability meaning that no college with no vacant positions can manipulate by dropping some of its filled positions. Our main result shows that the student-optimal stable mechanism is the unique stable mechanism which is non-Type-I-manipulable via capacities and independent of truncations. Our characterization supports the use of the student-optimal stable mechanism in these matching markets because of its limited manipulability via capacities by colleges.

Suggested Citation

  • EHLERS, Lars, 2009. "Manipulation via Capacities Revisited," Cahiers de recherche 04-2009, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    • Handle: RePEc:mtl:montec:04-2009
    as

    Download full text from publisher

    File URL: http://www.cireqmontreal.com/wp-content/uploads/cahiers/04-2009-cah.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Alcalde, Jose, 1996. "Implementation of Stable Solutions to Marriage Problems," Journal of Economic Theory, Elsevier, vol. 69(1), pages 240-254, April.
    2. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541, Elsevier.
    3. 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.
    4. Fuhito Kojima, 2006. "Mixed Strategies in Games of Capacity Manipulation in Hospital–Intern Markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 25-28, August.
    5. 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.
    6. Hideo Konishi & M. Ünver, 2006. "Games of Capacity Manipulation in Hospital-intern Markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 3-24, August.
    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. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November.
    9. Kojima Fuhito, 2007. "When Can Manipulations be Avoided in Two-Sided Matching Markets? -- Maximal Domain Results," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-18, September.
    10. Lars Ehlers, 2008. "Truncation Strategies in Matching Markets," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 327-335, May.
    11. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    12. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
    13. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
    14. Antonio Romero-Medina & Matteo Triossi, 2013. "Games with capacity manipulation: incentives and Nash equilibria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 701-720, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Antonio Romero-Medina & Matteo Triossi, 2013. "Games with capacity manipulation: incentives and Nash equilibria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 701-720, September.
    2. Vincent Iehlé & Julien Jacqmin, 2023. "SIGEM : analyse de la procédure d’affectation dans les grandes écoles de management," Revue économique, Presses de Sciences-Po, vol. 74(2), pages 139-168.
    3. Bonkoungou, Somouaoga & Nesterov, Alexander, 2023. "Incentives in matching markets: counting and comparing manipulating agents," Theoretical Economics, Econometric Society, vol. 18(3), July.
    4. Mustafa Oǧuz Afacan, 2016. "Characterizations of the cumulative offer process," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 531-542, October.
    5. Inácio Bó & C.-Philipp Heller, 2017. "Strategic schools under the Boston mechanism revisited," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 545-572, March.
    6. Afacan, Mustafa Oǧuz, 2013. "Application fee manipulations in matching markets," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 446-453.
    7. Azevedo, Eduardo M., 2014. "Imperfect competition in two-sided matching markets," Games and Economic Behavior, Elsevier, vol. 83(C), pages 207-223.
    8. Muto, Nozomu & Shirata, Yasuhiro, 2017. "Manipulation via endowments in auctions with multiple goods," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 75-84.
    9. Schummer, James & Abizada, Azar, 2017. "Incentives in landing slot problems," Journal of Economic Theory, Elsevier, vol. 170(C), pages 29-55.
    10. Hagen, Martin, 2022. "Tradable immigration quotas revisited," Journal of Public Economics, Elsevier, vol. 208(C).
    11. Assaf Romm, 2014. "Implications of capacity reduction and entry in many-to-one stable matching," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 851-875, December.
    12. Tommy Andersson & Lars Ehlers, 2020. "Assigning Refugees to Landlords in Sweden: Efficient, Stable, and Maximum Matchings," Scandinavian Journal of Economics, Wiley Blackwell, vol. 122(3), pages 937-965, July.

    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. Afacan, Mustafa Og̃uz & Dur, Umut Mert, 2017. "When preference misreporting is Harm[less]ful?," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 16-24.
    2. 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.
    3. Onur Kesten, 2012. "On two kinds of manipulation for school choice problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 677-693, November.
    4. Assaf Romm, 2014. "Implications of capacity reduction and entry in many-to-one stable matching," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 851-875, December.
    5. Afacan, Mustafa Oǧuz, 2016. "Enrollment manipulations in school choice," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 119-125.
    6. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    7. 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.
    8. Mehmet Ekmekci & M. Bumin Yenmez, "undated". "Integrating Schools for Centralized Admissions," GSIA Working Papers 2014-E20, Carnegie Mellon University, Tepper School of Business.
    9. 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.
    10. Hatfield, John William & Kojima, Fuhito & Narita, Yusuke, 2016. "Improving schools through school choice: A market design approach," Journal of Economic Theory, Elsevier, vol. 166(C), pages 186-211.
    11. Mustafa Afacan, 2014. "Fictitious students creation incentives in school choice problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 493-514, August.
    12. Inácio Bó & C.-Philipp Heller, 2017. "Strategic schools under the Boston mechanism revisited," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 545-572, March.
    13. Coles, Peter & Shorrer, Ran, 2014. "Optimal truncation in matching markets," Games and Economic Behavior, Elsevier, vol. 87(C), pages 591-615.
    14. Afacan, Mustafa Oǧuz, 2013. "Application fee manipulations in matching markets," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 446-453.
    15. Mustafa Afacan, 2013. "The welfare effects of pre-arrangements in matching markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(1), pages 139-151, May.
    16. Alvin E. Roth, 2009. "What Have We Learned from Market Design?," Innovation Policy and the Economy, University of Chicago Press, vol. 9(1), pages 79-112.
    17. EHLERS, Lars, 2010. "School Choice with Control," Cahiers de recherche 2010-05, Universite de Montreal, Departement de sciences economiques.
    18. John William Hatfield & Fuhito Kojima & Yusuke Narita, 2011. "Promoting School Competition Through School Choice: A Market Design Approach," Working Papers 2011-018, Human Capital and Economic Opportunity Working Group.
    19. 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.
    20. 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.

    More about this item

    Keywords

    Two-Sided Matching; Stability; Manipulation; Capacities;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • I20 - Health, Education, and Welfare - - Education - - - General

    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:mtl:montec:04-2009. 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: Sharon BREWER (email available below). General contact details of provider: https://edirc.repec.org/data/cdmtlca.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.