IDEAS home Printed from https://ideas.repec.org/p/bdm/wpaper/2020-03.html
   My bibliography  Save this paper

Many-to-one Matching: Externalities and Stability

Author

Listed:
  • Salgado Alfredo

Abstract

In this paper, we establish sufficient conditions on the domain of preferences and agents' behavior in order to characterize the existence of stable assignments in many-to-one matching problems with externalities. The set of stable matchings depends on what agents believe other agents will do if they deviate. Such sets of reactions are called estimation functions or simply estimations. We show that, unless some restrictions would be imposed on agents' preferences, there is no constraint on agents' behavior that assures the existence of stable matchings. In addition, we introduce a condition on preferences called bottom q-substitutability that guarantees the existence of at least one stable matching when the set of estimations includes all possible matches. Finally, we analyze a notion of the core and its relation with the set of stable assignments.

Suggested Citation

  • Salgado Alfredo, 2020. "Many-to-one Matching: Externalities and Stability," Working Papers 2020-03, Banco de México.
    • Handle: RePEc:bdm:wpaper:2020-03
    as

    Download full text from publisher

    File URL: https://www.banxico.org.mx/publications-and-press/banco-de-mexico-working-papers/%7B35DA1372-49AF-8651-C6BF-BA3A516CE535%7D.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rubinstein Ariel & Wolinsky Asher, 1994. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Games and Economic Behavior, Elsevier, vol. 6(2), pages 299-311, March.
    2. Shapley, Lloyd S & Shubik, Martin, 1969. "On the Core of an Economic System with Externalities," American Economic Review, American Economic Association, vol. 59(4), pages 678-684, Part I Se.
    3. Sasaki, Hiroo & Toda, Manabu, 1996. "Two-Sided Matching Problems with Externalities," Journal of Economic Theory, Elsevier, vol. 70(1), pages 93-108, July.
    4. Cantala, David, 2004. "Restabilizing matching markets at senior level," Games and Economic Behavior, Elsevier, vol. 48(1), pages 1-17, July.
    5. Yaron Azrieli, 2009. "On pure conjectural equilibrium with non-manipulable information," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 209-219, June.
    6. Echenique, Federico & Yenmez, M. Bumin, 2007. "A solution to matching with preferences over colleagues," Games and Economic Behavior, Elsevier, vol. 59(1), pages 46-71, April.
    7. 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.
    8. Kurucu, Gokce, 2007. "Negative Network Externalities in Two-Sided Markets: A Competition Approach," MPRA Paper 9746, University Library of Munich, Germany.
    9. Mumcu, Ayse & Saglam, Ismail, 2010. "Stable one-to-one matchings with externalities," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 154-159, September.
    10. Ismail Saglam & Ayse Mumcu, 2007. "The core of a housing market with externalities," Economics Bulletin, AccessEcon, vol. 3(57), pages 1-5.
    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. Bando, Keisuke, 2012. "Many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 14-20.
    2. 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.
    3. Aslan, Fatma & Lainé, Jean, 2020. "Competitive equilibria in Shapley–Scarf markets with couples," Journal of Mathematical Economics, Elsevier, vol. 89(C), pages 66-78.
    4. Fisher, James C.D. & Hafalir, Isa E., 2016. "Matching with aggregate externalities," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 1-7.
    5. Hong, Miho & Park, Jaeok, 2022. "Core and top trading cycles in a market with indivisible goods and externalities," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    6. Fonseca-Mairena, María Haydée & Triossi, Matteo, 2022. "Incentives and implementation in allocation problems with externalities," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    7. Mumcu, Ayse & Saglam, Ismail, 2010. "Stable one-to-one matchings with externalities," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 154-159, September.
    8. Doval, Laura, 2022. "Dynamically stable matching," Theoretical Economics, Econometric Society, vol. 17(2), May.
    9. Jens Gudmundsson & Helga Habis, 2017. "Assignment games with externalities revisited," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 247-257, October.
    10. AyÅŸe Mumcu & Ismail Saglam, 2021. "Strategic Issues in One-to-One Matching with Externalities," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 1-12, June.
    11. Bo Chen, 2019. "Downstream competition and upstream labor market matching," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(4), pages 1055-1085, December.
    12. Liu, Ce, 2018. "Stability in Repeated Matching Markets," Working Papers 2018-13, Michigan State University, Department of Economics.
    13. Alfredo Salgado-Torres, 2011. "A solution concept for housing market problems with externalities," Economics Bulletin, AccessEcon, vol. 31(1), pages 623-630.
    14. Ayse Mumcu & Ismail Saglam, 2019. "Strategic Issues in One-to-One Matching with Externalities Abstract:," Working Papers 2019/03, Bogazici University, Department of Economics.
    15. Bettina Klaus & Claudia Meo, 2023. "The core for housing markets with limited externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(3), pages 779-811, October.
    16. Chao Huang, 2021. "Stable matching: an integer programming approach," Papers 2103.03418, arXiv.org, revised Apr 2022.
    17. Imamura, Kenzo & Konishi, Hideo & Pan, Chen-Yu, 2023. "Stability in matching with externalities: Pairs competition and oligopolistic joint ventures," Journal of Economic Behavior & Organization, Elsevier, vol. 205(C), pages 270-286.
    18. Agnieszka Wiszniewska-Matyszkiel, 2016. "Belief distorted Nash equilibria: introduction of a new kind of equilibrium in dynamic games with distorted information," Annals of Operations Research, Springer, vol. 243(1), pages 147-177, August.
    19. Maria Gabriella Graziano & Claudia Meo & Nicholas C. Yannelis, 2020. "Shapley and Scarf housing markets with consumption externalities," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(5), pages 1481-1514, September.
    20. Dimitrov, Dinko & Lazarova, Emiliya A., 2008. "Coalitional Matchings," Coalition Theory Network Working Papers 37523, Fondazione Eni Enrico Mattei (FEEM).

    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

    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:bdm:wpaper:2020-03. 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: Subgerencia de desarrollo de sistemas (email available below). General contact details of provider: https://edirc.repec.org/data/bangvmx.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.