IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v147y2024icp533-553.html
   My bibliography  Save this article

Stability and substitutability in multi-period matching markets

Author

Listed:
  • Bando, Keisuke
  • Kawasaki, Ryo

Abstract

We analyze a multi-period matching market where matching between agents is decided for each time period. To analyze this situation, we embed the situation into the framework of many-to-many matching with contracts where the contract includes the time period at which the matching occurs. While a general stability concept is already defined for the matching with contracts framework, in a multi-period matching model, a stable outcome may not exist when contracts exhibit complementarities across time periods. Thus, we define a weaker stability concept called temporal stability by taking into account the dynamic nature of the model. We provide sufficient conditions for the existence of a temporally stable outcome, including a corresponding substitutability condition, ordered substitutability, for the multi-period matching model.

Suggested Citation

  • Bando, Keisuke & Kawasaki, Ryo, 2024. "Stability and substitutability in multi-period matching markets," Games and Economic Behavior, Elsevier, vol. 147(C), pages 533-553.
    • Handle: RePEc:eee:gamebe:v:147:y:2024:i:c:p:533-553
    DOI: 10.1016/j.geb.2024.08.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825624001180
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2024.08.013?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. 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.
    2. Damiano, Ettore & Lam, Ricky, 2005. "Stability in dynamic matching markets," Games and Economic Behavior, Elsevier, vol. 52(1), pages 34-53, July.
    3. 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.
    4. Sangram V. Kadam & Maciej H. Kotowski, 2018. "Multiperiod Matching," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(4), pages 1927-1947, November.
    5. 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.
    6. John Kennes Jr. & Daniel Monte Jr. & Norovsambuu Tumennasan Jr., 2014. "The Day Care Assignment: A Dynamic Matching Problem," American Economic Journal: Microeconomics, American Economic Association, vol. 6(4), pages 362-406, November.
    7. Kominers, Scott Duke & Sönmez, Tayfun, 2016. "Matching with slot-specific priorities: theory," Theoretical Economics, Econometric Society, vol. 11(2), May.
    8. Kotowski, Maciej, 2019. "A Perfectly Robust Approach to Multiperiod Matching Problems," Working Paper Series rwp19-016, Harvard University, John F. Kennedy School of Government.
    9. 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.
    10. Dimakopoulos, Philipp D. & Heller, C.-Philipp, 2019. "Matching with waiting times: The German entry-level labor market for lawyers," Games and Economic Behavior, Elsevier, vol. 115(C), pages 289-313.
    11. Christopher P. Chambers & M. Bumin Yenmez, 2017. "Choice and Matching," American Economic Journal: Microeconomics, American Economic Association, vol. 9(3), pages 126-147, August.
    12. 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.
    13. Umut Dur & Thayer Morrill & William Phan, 2024. "Partitionable choice functions and stability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(2), pages 359-375, September.
    14. 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.
    15. Pereyra, Juan Sebastián, 2013. "A dynamic school choice model," Games and Economic Behavior, Elsevier, vol. 80(C), pages 100-114.
    16. 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.
    17. Yenmez, M. Bumin, 2018. "A college admissions clearinghouse," Journal of Economic Theory, Elsevier, vol. 176(C), pages 859-885.
    18. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    19. Morimitsu Kurino, 2020. "Credibility, efficiency, and stability: a theory of dynamic matching markets," The Japanese Economic Review, Springer, vol. 71(1), pages 135-165, January.
    20. Chao Huang, 2021. "Unidirectional substitutes and complements," Papers 2108.12572, arXiv.org.
    21. John William Hatfield & Scott Duke Kominers & Alexander Westkamp, 2021. "Stability, Strategy-Proofness, and Cumulative Offer Mechanisms [Stability and Incentives for College Admissions with Budget Constraints]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(3), pages 1457-1502.
    22. Liu, Ce, 2023. "Stability in repeated matching markets," Theoretical Economics, Econometric Society, vol. 18(4), November.
    23. Hirata, Daisuke & Kasuya, Yusuke, 2014. "Cumulative offer process is order-independent," Economics Letters, Elsevier, vol. 124(1), pages 37-40.
    24. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    25. Dur, Umut & Morrill, Thayer & Phan, William, 2022. "Family ties: school assignment with siblings," Theoretical Economics, Econometric Society, vol. 17(1), January.
    26. Kadam, Sangram V. & Kotowski, Maciej H., 2018. "Time horizons, lattice structures, and welfare in multi-period matching markets," Games and Economic Behavior, Elsevier, vol. 112(C), pages 1-20.
    27. Dean Corbae & Ted Temzelides & Randall Wright, 2003. "Directed Matching and Monetary Exchange," Econometrica, Econometric Society, vol. 71(3), pages 731-756, May.
    28. Doval, Laura, 2022. "Dynamically stable matching," Theoretical Economics, Econometric Society, vol. 17(2), May.
    29. Gale, Douglas, 1978. "The core of a monetary economy without trust," Journal of Economic Theory, Elsevier, vol. 19(2), pages 456-491, December.
    30. Gonczarowski, Yannai A. & Kominers, Scott Duke & Shorrer, Ran I., 0. "To infinity and beyond: a general framework for scaling economic theories," Theoretical Economics, Econometric Society.
    31. Orhan Ayg?n & Tayfun S?nmez, 2013. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 103(5), pages 2050-2051, August.
    32. Bando, Keisuke & Hirai, Toshiyuki & Zhang, Jun, 2021. "Substitutes and stability for many-to-many matching with contracts," Games and Economic Behavior, Elsevier, vol. 129(C), pages 503-512.
    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. Kadam, Sangram V. & Kotowski, Maciej H., 2018. "Time horizons, lattice structures, and welfare in multi-period matching markets," Games and Economic Behavior, Elsevier, vol. 112(C), pages 1-20.
    2. 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).
    3. Avataneo, Michelle & Turhan, Bertan, 2021. "Slot-specific priorities with capacity transfers," Games and Economic Behavior, Elsevier, vol. 129(C), pages 536-548.
    4. Schlegel, Jan Christoph, 2020. "Equivalent choice functions and stable mechanisms," Games and Economic Behavior, Elsevier, vol. 123(C), pages 41-53.
    5. Bando, Keisuke & Hirai, Toshiyuki & Zhang, Jun, 2021. "Substitutes and stability for many-to-many matching with contracts," Games and Economic Behavior, Elsevier, vol. 129(C), pages 503-512.
    6. Schlegel, Jan Christoph, 2015. "Contracts versus salaries in matching: A general result," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 552-573.
    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. 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.
    9. Klijn, Flip & Yazıcı, Ayşe, 2014. "A many-to-many ‘rural hospital theorem’," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 63-73.
    10. Yenmez, M. Bumin, 2018. "A college admissions clearinghouse," Journal of Economic Theory, Elsevier, vol. 176(C), pages 859-885.
    11. Dimakopoulos, Philipp D. & Heller, C.-Philipp, 2019. "Matching with waiting times: The German entry-level labor market for lawyers," Games and Economic Behavior, Elsevier, vol. 115(C), pages 289-313.
    12. Tam'as Fleiner & Zsuzsanna Jank'o & Akihisa Tamura & Alexander Teytelboym, 2015. "Trading Networks with Bilateral Contracts," Papers 1510.01210, arXiv.org, revised May 2018.
    13. Alva, Samson, 2018. "WARP and combinatorial choice," Journal of Economic Theory, Elsevier, vol. 173(C), pages 320-333.
    14. Aygün, Orhan & Turhan, Bertan, 2020. "Dynamic reserves in matching markets," Journal of Economic Theory, Elsevier, vol. 188(C).
    15. 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.
    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. Jagadeesan, Ravi, 2018. "Lone wolves in infinite, discrete matching markets," Games and Economic Behavior, Elsevier, vol. 108(C), pages 275-286.
    18. 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.
    19. Adachi, Hiroyuki, 2017. "Stable matchings and fixed points in trading networks: A note," Economics Letters, Elsevier, vol. 156(C), pages 65-67.
    20. Morimitsu Kurino, 2020. "Credibility, efficiency, and stability: a theory of dynamic matching markets," The Japanese Economic Review, Springer, vol. 71(1), pages 135-165, January.

    More about this item

    Keywords

    Multi-period matching; Matching with contracts; Temporal stability; Ordered substitutability;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    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:gamebe:v:147:y:2024:i:c:p:533-553. 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/inca/622836 .

    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.