IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v146y2016icp85-88.html
   My bibliography  Save this article

Matching with contracts, substitutes and two-unit demand

Author

Listed:
  • Tello, Benjamín

Abstract

In the context of many-to-one matching with contracts, we show that for any choice function that satisfies the irrelevance of rejected contracts condition (Aygün and Sönmez, 2013) and selects at most two contracts from any given set of contracts (two-unit demand), bilateral substitutability and weak substitutability are equivalent. As a corollary, we obtain a new maximal domain for the existence of stable matchings in the unit-capacity couples model. Finally, we show with an example that the equivalence between bilateral and weak substitutability crucially depends on the two-unit demand condition.

Suggested Citation

  • Tello, Benjamín, 2016. "Matching with contracts, substitutes and two-unit demand," Economics Letters, Elsevier, vol. 146(C), pages 85-88.
    • Handle: RePEc:eee:ecolet:v:146:y:2016:i:c:p:85-88
    DOI: 10.1016/j.econlet.2016.07.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176516302567
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2016.07.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
    2. Bettina Klaus & Flip Klijn & Toshifumi Nakamura, 2005. "Corrigendum: Stable Matchings and Preferences of Couples," Working Papers 261, Barcelona School of Economics.
    3. Parag A. Pathak & Alvin E. Roth, 2013. "Matching with Couples: Stability and Incentives in Large Markets," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(4), pages 1585-1632.
    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. , Emin & , Bumin & , Ali, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
    6. John William Hatfield & Fuhito Kojima, 2008. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 98(3), pages 1189-1194, June.
    7. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    8. 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.
    9. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July.
    10. Itai Ashlagi & Mark Braverman & Avinatan Hassidim, 2014. "Stability in Large Matching Markets with Complementarities," Operations Research, INFORMS, vol. 62(4), pages 713-732, August.
    11. Orhan Ayg?n & Tayfun S?nmez, 2013. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 103(5), pages 2050-2051, August.
    12. 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.
    13. Orhan Aygün & Tayfun Sönmez, 2012. "The Importance of Irrelevance of Rejected Contracts in Matching under Weakened Substitutes Conditions," Boston College Working Papers in Economics 805, Boston College Department of Economics.
    14. Thanh Nguyen & Rakesh Vohra, 2014. "Near Feasible Stable Matchings with Complementarities," PIER Working Paper Archive 14-028, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    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. Yang, Yi-You, 2020. "Rationalizable choice functions," Games and Economic Behavior, Elsevier, vol. 123(C), pages 120-126.
    2. Benjamin Tello, 2022. "Stability and Contractual Efficiency in Matching with Contracts and Lexicographic Preferences," Economics Bulletin, AccessEcon, vol. 42(1), pages 41-48.
    3. Tello, Benjamín, 2023. "Restricted complementarity and paths to stability in matching with couples," Mathematical Social Sciences, Elsevier, vol. 126(C), pages 60-67.
    4. Benjamín Tello, 2023. "Restricted Complementarity and Paths to Stability in Matching with Couples," CEMLA Working Paper Series 02/2023, CEMLA.

    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. 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.
    2. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 33(4), pages 541-571.
    3. Kojima, Fuhito & Tamura, Akihisa & Yokoo, Makoto, 2018. "Designing matching mechanisms under constraints: An approach from discrete convex analysis," Journal of Economic Theory, Elsevier, vol. 176(C), pages 803-833.
    4. Hafalir, Isa E. & Kojima, Fuhito & Yenmez, M. Bumin, 2022. "Interdistrict school choice: A theory of student assignment," Journal of Economic Theory, Elsevier, vol. 201(C).
    5. Chao Huang, 2022. "Two-sided matching with firms' complementary preferences," Papers 2205.05599, arXiv.org, revised May 2022.
    6. Péter Biró & Flip Klijn, 2013. "Matching With Couples: A Multidisciplinary Survey," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-18.
    7. Chao Huang, 2022. "Firm-worker hypergraphs," Papers 2211.06887, arXiv.org, revised Nov 2023.
    8. Avataneo, Michelle & Turhan, Bertan, 2021. "Slot-specific priorities with capacity transfers," Games and Economic Behavior, Elsevier, vol. 129(C), pages 536-548.
    9. Benjamín Tello, 2023. "Restricted Complementarity and Paths to Stability in Matching with Couples," CEMLA Working Paper Series 02/2023, CEMLA.
    10. Afacan, Mustafa Oǧuz, 2020. "Graduate admission with financial support," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 114-127.
    11. Chao Huang, 2021. "Stable matching: an integer programming approach," Papers 2103.03418, arXiv.org, revised Apr 2022.
    12. Aygün, Orhan & Turhan, Bertan, 2020. "Dynamic reserves in matching markets," Journal of Economic Theory, Elsevier, vol. 188(C).
    13. Yenmez, M. Bumin, 2018. "A college admissions clearinghouse," Journal of Economic Theory, Elsevier, vol. 176(C), pages 859-885.
    14. 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.
    15. Schlegel, Jan Christoph, 2020. "Equivalent choice functions and stable mechanisms," Games and Economic Behavior, Elsevier, vol. 123(C), pages 41-53.
    16. Tayfun Sönmez, 2013. "Bidding for Army Career Specialties: Improving the ROTC Branching Mechanism," Journal of Political Economy, University of Chicago Press, vol. 121(1), pages 186-219.
    17. 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.
    18. Ata Atay & Sylvain Funck & Ana Mauleon & Vincent Vannetelbosch, 2023. "Matching markets with farsighted couples," Papers 2304.12276, arXiv.org, revised Apr 2023.
    19. Afacan, Mustafa Oǧuz, 2017. "Some further properties of the cumulative offer process," Games and Economic Behavior, Elsevier, vol. 104(C), pages 656-665.
    20. Kadam, Sangram Vilasrao, 2017. "Unilateral substitutability implies substitutable completability in many-to-one matching with contracts," Games and Economic Behavior, Elsevier, vol. 102(C), pages 56-68.

    More about this item

    Keywords

    Matching; Contracts; Stability; Couples; Weak substitutability; Bilateral substitutability;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

    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:eee:ecolet:v:146:y:2016:i:c:p:85-88. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    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.