IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2405.07084.html
   My bibliography  Save this paper

Counting steps for re-stabilization in a labor matching market

Author

Listed:
  • Agustin G. Bonifacio
  • Nadia Gui~nazu
  • Noelia Juarez
  • Pablo Neme
  • Jorge Oviedo

Abstract

We study a one-to-one labor matching market. If a worker considers resigning from her current job to obtain a better one, how long does it take for this worker to actually get it? We present an algorithm that models this situation as a re-stabilization process involving a vacancy chain. Each step of the algorithm is a link of such a chain. We show that the length of this vacancy chain, which can be interpreted as the time the worker has to wait for her new job, is intimately connected with the lattice structure of the set of stable matchings of the market. Namely, this length can be computed by considering the cardinalities of cycles in preferences derived from the initial and final stable matchings involved.

Suggested Citation

  • Agustin G. Bonifacio & Nadia Gui~nazu & Noelia Juarez & Pablo Neme & Jorge Oviedo, 2024. "Counting steps for re-stabilization in a labor matching market," Papers 2405.07084, arXiv.org.
    • Handle: RePEc:arx:papers:2405.07084
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2405.07084
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Cantala, David, 2004. "Restabilizing matching markets at senior level," Games and Economic Behavior, Elsevier, vol. 48(1), pages 1-17, July.
    2. Blum, Yosef & Roth, Alvin E. & Rothblum, Uriel G., 1997. "Vacancy Chains and Equilibration in Senior-Level Labor Markets," Journal of Economic Theory, Elsevier, vol. 76(2), pages 362-411, October.
    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. Raïssa-Juvette Samba Zitou & Rhonya Adli, 2012. "Quasi stable outcomes in the assignment game," Theory and Decision, Springer, vol. 72(3), pages 323-340, March.
    2. Francis Bloch & David Cantala, 2013. "Markovian assignment rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 1-25, January.
    3. Elette Boyle & Federico Echenique, 2009. "Sequential entry in many-to-one matching markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(1), pages 87-99, June.
    4. 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.
    5. Ayse Yazici, 2022. "Decentralized Matching at Senior-Level: Stability and Incentives," Working Papers 2022_01, Durham University Business School.
    6. Beatriz Millán & Eliana Pepa Risma, 2018. "Random path to stability in a decentralized market with contracts," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 79-103, June.
    7. Saglam, Ismail, 2019. "Measuring the External Stability of the One-to-One Matching Generated by the Deferred Acceptance Algorithm," MPRA Paper 91472, University Library of Munich, Germany.
    8. Mill'an Guerra Beatriz Alejandra, 2022. "The outcome of the restabilization process in matching markets," Papers 2202.12452, arXiv.org.
    9. Ismail Saglam, 2020. "Measuring external stability in one-to-one matching," Economics Bulletin, AccessEcon, vol. 40(1), pages 234-247.
    10. David Cantala, 2011. "Agreement toward stability in matching markets," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 293-316, December.
    11. Yazıcı, Ayşe, 2022. "Decentralized matching at senior-level: Stability and incentives," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    12. Ehlers, Lars & Hafalir, Isa E. & Yenmez, M. Bumin & Yildirim, Muhammed A., 2014. "School choice with controlled choice constraints: Hard bounds versus soft bounds," Journal of Economic Theory, Elsevier, vol. 153(C), pages 648-683.
    13. Rodríguez-Álvarez, Carmelo & Romero-Medina, Antonio, 2024. "School choice with transferable student characteristics," Games and Economic Behavior, Elsevier, vol. 143(C), pages 103-124.
    14. Yuen Leng Chow & Isa E. Hafalir & Abdullah Yavas, 2015. "Auction versus Negotiated Sale: Evidence from Real Estate Sales," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 43(2), pages 432-470, June.
    15. Damiano, Ettore & Lam, Ricky, 2005. "Stability in dynamic matching markets," Games and Economic Behavior, Elsevier, vol. 52(1), pages 34-53, July.
    16. Péter Biró & Katarína Cechlárová & Tamás Fleiner, 2008. "The dynamics of stable matchings and half-matchings for the stable marriage and roommates problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 333-352, March.
    17. Jean J. GABSZEWICZ & Filomena, GARCIA & Joana, PAIS & Joana, RESENDE, 2008. "On Gale and Shapley ‘College admissions and stability of marriage’," Discussion Papers (ECON - Département des Sciences Economiques) 2008046, Université catholique de Louvain, Département des Sciences Economiques.
    18. Fisher, James C.D. & Hafalir, Isa E., 2016. "Matching with aggregate externalities," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 1-7.
    19. Ozan Candogan & Markos Epitropou & Rakesh V. Vohra, 2021. "Competitive Equilibrium and Trading Networks: A Network Flow Approach," Operations Research, INFORMS, vol. 69(1), pages 114-147, January.
    20. Yasushi Kawase & Keisuke Bando, 2021. "Subgame perfect equilibria under the deferred acceptance algorithm," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 503-546, June.

    More about this item

    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

    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:arx:papers:2405.07084. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.