IDEAS home Printed from https://ideas.repec.org/p/lau/crdeep/17.01.html
   My bibliography  Save this paper

Non-Revelation Mechanisms for Many-to-Many Matching: Equilibria versus Stability

Author

Listed:
  • Bettina Klaus
  • Flip Klijn

Abstract

We study many-to-many matching markets in which agents from a set A are matched to agents from a disjoint set B through a two-stage non-revelation mechanism. In the first stage, A-agents, who are endowed with a quota that describes the maximal number of agents they can be matched to, simultaneously make proposals to the B-agents. In the second stage,B-agents sequentially, and respecting the quota, choose and match to available A-proposers. We study the subgame perfect Nash equilibria of the induced game. We prove that stable matchings are equilibrium outcomes if all A-agents' preferences are substitutable. We also show that the implementation of the set of stable matchings is closely related to the quotas of the A-agents. In particular, implementation holds when A-agents' preferences are substitutable and their quotas are non-binding.

Suggested Citation

  • Bettina Klaus & Flip Klijn, 2017. "Non-Revelation Mechanisms for Many-to-Many Matching: Equilibria versus Stability," Cahiers de Recherches Economiques du Département d'économie 17.01, Université de Lausanne, Faculté des HEC, Département d’économie.
  • Handle: RePEc:lau:crdeep:17.01
    as

    Download full text from publisher

    File URL: http://hec.unil.ch/attachments/deep/series/2016/17.01.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Antonio Romero-Medina & Matteo Triossi, 2017. "Take-it-or-leave-it contracts in many-to-many matching markets," Documentos de Trabajo 328, Centro de Economía Aplicada, Universidad de Chile.
    2. Charles Blair, 1988. "The Lattice Structure of the Set of Stable Matchings with Multiple Partners," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 619-628, November.
    3. Echenique, Federico & Oviedo, Jorge, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    4. Alcalde, Jose & Romero-Medina, Antonio, 2000. "Simple Mechanisms to Implement the Core of College Admissions Problems," Games and Economic Behavior, Elsevier, vol. 31(2), pages 294-302, May.
    5. Romero-Medina, Antonio & Triossi, Matteo, 2014. "Non-revelation mechanisms in many-to-one markets," Games and Economic Behavior, Elsevier, vol. 87(C), pages 624-630.
    6. Vulkan, Nir & Roth, Alvin E. & Neeman, Zvika (ed.), 2013. "The Handbook of Market Design," OUP Catalogue, Oxford University Press, number 9780199570515.
    7. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    8. Marilda Sotomayor, 2003. "Reaching the core of the marriage market through a non-revelation matching mechanism," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(2), pages 241-251, December.
    9. 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.
    10. Sotomayor, Marilda, 2004. "Implementation in the many-to-many matching market," Games and Economic Behavior, Elsevier, vol. 46(1), pages 199-212, January.
    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, 2017. "Take-it-or-leave-it contracts in many-to-many matching markets," Documentos de Trabajo 328, Centro de Economía Aplicada, Universidad de Chile.
    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.

    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. 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.
    2. 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.
    3. Antonio Romero-Medina & Matteo Triossi, 2017. "Take-it-or-leave-it contracts in many-to-many matching markets," Documentos de Trabajo 328, Centro de Economía Aplicada, Universidad de Chile.
    4. 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.
    5. Paula Jaramillo & Çaǧatay Kayı & Flip Klijn, 2014. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 793-811, April.
    6. Westkamp, Alexander, 2010. "Market Structure and Matching with Contracts," Bonn Econ Discussion Papers 02/2010, University of Bonn, Bonn Graduate School of Economics (BGSE).
    7. Klijn, Flip & Yazıcı, Ayşe, 2014. "A many-to-many ‘rural hospital theorem’," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 63-73.
    8. Tamás Fleiner & Ravi Jagadeesan & Zsuzsanna Jankó & Alexander Teytelboym, 2019. "Trading Networks With Frictions," Econometrica, Econometric Society, vol. 87(5), pages 1633-1661, September.
    9. Danilov, V., 2021. "Stable systems of schedule contracts," Journal of the New Economic Association, New Economic Association, vol. 51(3), pages 12-29.
    10. Hideo Konishi & M. Utku Ünver, 2003. "Credible Group Stability in Multi-Partner Matching Problems," Working Papers 2003.115, Fondazione Eni Enrico Mattei.
    11. John William Hatfield & Scott Duke Kominers, 2012. "Matching in Networks with Bilateral Contracts," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 176-208, February.
    12. Ayşe Yazıcı, 2017. "Probabilistic stable rules and Nash equilibrium in two-sided matching problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 103-124, March.
    13. 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.
    14. Andersson, Tommy & Dur, Umut & Ertemel, Sinan & Kesten , Onur, 2018. "Sequential School Choice with Public and Private Schools," Working Papers 2018:39, Lund University, Department of Economics.
    15. Tam'as Fleiner & Zsuzsanna Jank'o & Akihisa Tamura & Alexander Teytelboym, 2015. "Trading Networks with Bilateral Contracts," Papers 1510.01210, arXiv.org, revised May 2018.
    16. Jiao, Zhenhua & Tian, Guoqiang, 2017. "The Blocking Lemma and strategy-proofness in many-to-many matchings," Games and Economic Behavior, Elsevier, vol. 102(C), pages 44-55.
    17. Daniel Lehmann, 2019. "Revealed Preferences for Matching with Contracts," Papers 1908.08823, arXiv.org, revised Mar 2020.
    18. Alfredo Salgado, 2018. "Incomplete Information and Costly Signaling in College Admissions," Working Papers 2018-23, Banco de México.
    19. 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.
    20. Kucuksenel Serkan, 2011. "Implementation of the Core in College Admissions Problems When Colleagues Matter," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-14, September.

    More about this item

    Keywords

    implementation; matching; mechanisms; stability; substitutability;
    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

    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:lau:crdeep:17.01. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/deelsch.html .

    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: Michèle Jaccoud Ramseier (email available below). General contact details of provider: https://edirc.repec.org/data/deelsch.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.