IDEAS home Printed from https://ideas.repec.org/p/col/000092/009997.html
   My bibliography  Save this paper

On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets

Author

Listed:
  • Paula Jaramillo
  • Kagi Cagatay
  • Flip Klijn

Abstract

We consider two-sided many-to-many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market. We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshu_ing).We study when truncation / dropping strategies are exhaustive for a group of agents on the same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation / dropping strategies. We prove that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 1). We show that this result cannot be extended neither to group manipulations (even when all quotas equal 1 - Example 1), nor to individual manipulations when the agent's quota is larger than 1 (even when all other agents' quotas equal 1 - Example 2). Finally, we prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 2), i.e., independently of the quotas.

Suggested Citation

  • Paula Jaramillo & Kagi Cagatay & Flip Klijn, 2012. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," Documentos de Trabajo 9997, Universidad del Rosario.
  • Handle: RePEc:col:000092:009997
    as

    Download full text from publisher

    File URL: http://repository.urosario.edu.co/bitstream/handle/10336/10830/9997.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Tamás Fleiner, 2003. "A Fixed-Point Approach to Stable Matchings and Some Applications," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 103-126, February.
    2. Klijn, Flip & Yazıcı, Ayşe, 2014. "A many-to-many ‘rural hospital theorem’," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 63-73.
    3. Konishi, Hideo & Unver, M. Utku, 2006. "Credible group stability in many-to-many matching problems," Journal of Economic Theory, Elsevier, vol. 129(1), pages 57-80, July.
    4. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2004. "An algorithm to compute the full set of many-to-many stable matchings," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 187-210, March.
    5. Coles, Peter & Shorrer, Ran, 2014. "Optimal truncation in matching markets," Games and Economic Behavior, Elsevier, vol. 87(C), pages 591-615.
    6. Ma, Jinpeng, 2010. "The singleton core in the college admissions problem and its application to the National Resident Matching Program (NRMP)," Games and Economic Behavior, Elsevier, vol. 69(1), pages 150-164, May.
    7. Lars Ehlers, 2008. "Truncation Strategies in Matching Markets," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 327-335, May.
    8. 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.
    9. Ahmet Alkan, 2001. "original papers : On preferences over subsets and the lattice structure of stable matchings," Review of Economic Design, Springer;Society for Economic Design, vol. 6(1), pages 99-111.
    10. 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.
    11. 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.
    12. Ahmet Alkan, 2002. "A class of multipartner matching markets with a strong lattice structure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 737-746.
    13. , & ,, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    14. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    15. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    16. Marilda Sotomayor, 1999. "The lattice structure of the set of stable outcomes of the multiple partners assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 567-583.
    17. 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.
    18. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
    19. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November.
    20. 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.
    21. Itai Ashlagi & Flip Klijn, 2012. "Manipulability in matching markets: conflict and coincidence of interests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(1), pages 23-33, June.
    22. Roth, Alvin E & Sotomayor, Marilda, 1989. "The College Admissions Problem Revisited," Econometrica, Econometric Society, vol. 57(3), pages 559-570, May.
    23. Ruth Mart?ez & Jordi MassóAuthor-Name: Alejandro Neme & Jorge Oviedo, "undated". "An Algorithm To Compute The Set Of Many-To-Many Stable Matchings," UFAE and IAE Working Papers 457.00, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    24. 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.
    25. Roth, Alvin E, 1991. "A Natural Experiment in the Organization of Entry-Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom," American Economic Review, American Economic Association, vol. 81(3), pages 415-440, June.
    26. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
    27. Mongell, Susan & Roth, Alvin E, 1991. "Sorority Rush as a Two-Sided Matching Mechanism," American Economic Review, American Economic Association, vol. 81(3), pages 441-464, June.
    28. Alvin E. Roth & Uriel G. Rothblum, 1999. "Truncation Strategies in Matching Markets--In Search of Advice for Participants," Econometrica, Econometric Society, vol. 67(1), pages 21-44, January.
    29. Roth, Alvin E & Vande Vate, John H, 1991. "Incentives in Two-Sided Matching with Random Stable Mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 31-44, January.
    30. 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. Klijn, Flip & Pais, Joana & Vorsatz, Marc, 2019. "Static versus dynamic deferred acceptance in school choice: Theory and experiment," Games and Economic Behavior, Elsevier, vol. 113(C), pages 147-163.
    2. Jaramillo, Paula & Kayı, Çaǧatay & Klijn, Flip, 2013. "Equilibria under deferred acceptance: Dropping strategies, filled positions, and welfare," Games and Economic Behavior, Elsevier, vol. 82(C), pages 693-701.
    3. Klijn, Flip & Yazıcı, Ayşe, 2014. "A many-to-many ‘rural hospital theorem’," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 63-73.

    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. 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.
    2. Klijn, Flip & Yazıcı, Ayşe, 2014. "A many-to-many ‘rural hospital theorem’," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 63-73.
    3. 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.
    4. 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.
    5. Tam'as Fleiner & Zsuzsanna Jank'o & Akihisa Tamura & Alexander Teytelboym, 2015. "Trading Networks with Bilateral Contracts," Papers 1510.01210, arXiv.org, revised May 2018.
    6. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    7. 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.
    8. Ma, Jinpeng, 2010. "The singleton core in the college admissions problem and its application to the National Resident Matching Program (NRMP)," Games and Economic Behavior, Elsevier, vol. 69(1), pages 150-164, May.
    9. 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.
    10. 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.
    11. 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.
    12. Itai Ashlagi & Flip Klijn, 2012. "Manipulability in matching markets: conflict and coincidence of interests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(1), pages 23-33, June.
    13. Jaramillo, Paula & Kayı, Çaǧatay & Klijn, Flip, 2013. "Equilibria under deferred acceptance: Dropping strategies, filled positions, and welfare," Games and Economic Behavior, Elsevier, vol. 82(C), pages 693-701.
    14. Konishi, Hideo & Unver, M. Utku, 2006. "Credible group stability in many-to-many matching problems," Journal of Economic Theory, Elsevier, vol. 129(1), pages 57-80, July.
    15. Coles, Peter & Shorrer, Ran, 2014. "Optimal truncation in matching markets," Games and Economic Behavior, Elsevier, vol. 87(C), pages 591-615.
    16. 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.
    17. Juárez, Noelia & Neme, Pablo & Oviedo, Jorge, 2022. "Lattice structure of the random stable set in many-to-many matching markets," Games and Economic Behavior, Elsevier, vol. 132(C), pages 255-273.
    18. Hideo Konishi & M. Utku Ünver, 2003. "Credible Group Stability in Multi-Partner Matching Problems," Working Papers 2003.115, Fondazione Eni Enrico Mattei.
    19. 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.
    20. Yuichiro Kamada & Fuhito Kojima, 2020. "Accommodating various policy goals in matching with constraints," The Japanese Economic Review, Springer, vol. 71(1), pages 101-133, January.

    More about this item

    Keywords

    matching; many{to-many; stability; manipulability; truncation strategies; dropping strategies.;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D60 - Microeconomics - - Welfare Economics - - - General

    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:col:000092:009997. 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: Facultad de Economía (email available below). General contact details of provider: https://edirc.repec.org/data/ferosco.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.