IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v91y2020icp136-140.html
   My bibliography  Save this article

Existence of stable allocations in matching markets with infinite contracts: A topological approach

Author

Listed:
  • Fisher, James C.D.

Abstract

In classic matching markets, individuals choose their partners and each pair chooses a contract from a finite set of feasible contracts; the existence of stable allocations then follows from the (generalized) Deferred Acceptance algorithm. We consider an extension where the contract set is a compact subset of a topological vector space (e.g., Rk or ℂ[0,1]) and give a simple topological argument, which leverages this classic algorithm, to establish the existence of stable allocations when payoffs are upper-semicontinuous.

Suggested Citation

  • Fisher, James C.D., 2020. "Existence of stable allocations in matching markets with infinite contracts: A topological approach," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 136-140.
    • Handle: RePEc:eee:mateco:v:91:y:2020:i:c:p:136-140
    DOI: 10.1016/j.jmateco.2020.09.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406820301026
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2020.09.005?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. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    2. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-888, July.
    3. 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.
    4. Chen, Ning & Li, Mengling, 2019. "Pareto stability in two-sided many-to-many matching with weak preferences," Journal of Mathematical Economics, Elsevier, vol. 82(C), pages 272-284.
    5. Mongell, Susan J. & Roth, Alvin E., 1986. "A note on job matching with budget constraints," Economics Letters, Elsevier, vol. 21(2), pages 135-138.
    6. Kaneko, Mamoru, 1982. "The central assignment game and the assignment markets," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 205-232, September.
    7. Marek Pycia & M Bumin Yenmez, 2023. "Matching with Externalities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(2), pages 948-974.
    8. Fisher, James C.D. & Hafalir, Isa E., 2016. "Matching with aggregate externalities," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 1-7.
    9. Alkan, Ahmet & Gale, David, 1990. "The core of the matching game," Games and Economic Behavior, Elsevier, vol. 2(3), pages 203-212, September.
    10. Ortega, Josué, 2018. "Social integration in two-sided matching markets," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 119-126.
    11. , Emin & , Bumin & , Ali, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
    12. Martínez, Ruth & Massó, Jordi & Neme, Alejandro & Oviedo, Jorge, 2010. "The Blocking Lemma for a many-to-one matching model," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 937-949, September.
    13. Dur, Umut Mert & Wiseman, Thomas, 2019. "School choice with neighbors," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 101-109.
    14. Yeon‐Koo Che & Jinwoo Kim & Fuhito Kojima, 2019. "Stable Matching in Large Economies," Econometrica, Econometric Society, vol. 87(1), pages 65-110, January.
    15. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    16. Afacan, Mustafa Oǧuz, 2013. "Application fee manipulations in matching markets," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 446-453.
    17. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    18. , & ,, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    19. 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.
    20. Tamás Fleiner & Ravi Jagadeesan & Zsuzsanna Jankó & Alexander Teytelboym, 2019. "Trading Networks With Frictions," Econometrica, Econometric Society, vol. 87(5), pages 1633-1661, September.
    21. Abizada, Azar, 2016. "Stability and incentives for college admissions with budget constraints," Theoretical Economics, Econometric Society, vol. 11(2), May.
    22. Chiappori, Pierre-André & Reny, Philip J., 2016. "Matching to share risk," Theoretical Economics, Econometric Society, vol. 11(1), January.
    23. Kitahara, Minoru & Okumura, Yasunori, 2019. "On the number of employed in the matching model," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 63-69.
    24. Bando, Keisuke, 2014. "A modified deferred acceptance algorithm for many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 173-181.
    25. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    26. Eduardo M. Azevedo & Jacob D. Leshno, 2016. "A Supply and Demand Framework for Two-Sided Matching Markets," Journal of Political Economy, University of Chicago Press, vol. 124(5), pages 1235-1268.
    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. Shi, Fanqi, 2021. "Stability in sequential matching with incomplete information," Games and Economic Behavior, Elsevier, vol. 129(C), pages 492-502.

    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. Herings, P. Jean-Jacques, 2024. "Expectational equilibria in many-to-one matching models with contracts," Journal of Economic Theory, Elsevier, vol. 216(C).
    2. Alfred Galichon & Simon Weber, 2024. "Matching under Imperfectly Transferable Utility," Papers 2403.05222, arXiv.org, revised Oct 2024.
    3. Tam'as Fleiner & Zsuzsanna Jank'o & Akihisa Tamura & Alexander Teytelboym, 2015. "Trading Networks with Bilateral Contracts," Papers 1510.01210, arXiv.org, revised May 2018.
    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. 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.
    6. Yenmez, M. Bumin, 2018. "A college admissions clearinghouse," Journal of Economic Theory, Elsevier, vol. 176(C), pages 859-885.
    7. Kominers, Scott Duke & Hatfield, John William & Nichifor, Alexandru & Ostrovsky, Michael & Westkamp, Alexander, 2021. "Chain stability in trading networks," Theoretical Economics, Econometric Society, vol. 16(1), January.
    8. P. Jean‐Jacques Herings & Yu Zhou, 2022. "Competitive Equilibria In Matching Models With Financial Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(2), pages 777-802, May.
    9. Alfred Galichon & Scott Kominers & Simon Weber, 2014. "An Empirical Framework for Matching with Imperfectly Transferable Utility," Working Papers hal-03460155, HAL.
    10. Jonathan Ma & Scott Duke Kominers, 2018. "Bundling Incentives in (Many-to-Many) Matching with Contracts," Harvard Business School Working Papers 19-011, Harvard Business School.
    11. Yu Zhou & Shigehiro Serizawa, 2020. "Serial Vickrey Mechanism," ISER Discussion Paper 1095, Institute of Social and Economic Research, Osaka University.
    12. Tamás Fleiner & Ravi Jagadeesan & Zsuzsanna Jankó & Alexander Teytelboym, 2019. "Trading Networks With Frictions," Econometrica, Econometric Society, vol. 87(5), pages 1633-1661, September.
    13. repec:hal:spmain:info:hdl:2441/5kmb4ke32h9ur9159sab6hvkck is not listed on IDEAS
    14. Alfred Galichon & Scott Kominers & Simon Weber, 2014. "An Empirical Framework for Matching with Imperfectly Transferable Utility," Working Papers hal-03460155, HAL.
    15. 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.
    16. Hatfield, John William & Kominers, Scott Duke, 2015. "Multilateral matching," Journal of Economic Theory, Elsevier, vol. 156(C), pages 175-206.
    17. 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.
    18. 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.
    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. 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.
    21. Herings, P. Jean-Jacques, 2020. "Expectational Equilibria in Many-to-one Matching Models with Contracts - A Reformulation of Competitive Equilibrium," Research Memorandum 018, Maastricht University, Graduate School of Business and Economics (GSBE).

    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:mateco:v:91:y:2020:i:c:p:136-140. 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/jmateco .

    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.