Advanced Search
MyIDEAS: Login to save this article or follow this journal

Analysis of stochastic matching markets

Contents:

Author Info

  • Péter Biró

    ()

  • Gethin Norman

    ()

Registered author(s):

    Abstract

    Suppose that the agents of a matching market contact each other randomly and form new pairs if is in their interest. Does such a process always converge to a stable matching if one exists? If so, how quickly? Are some stable matchings more likely to be obtained by this process than others? In this paper we are going to provide answers to these and similar questions, posed by economists and computer scientists. In the first part of the paper we give an alternative proof for the theorems by Diamantoudi et al. and Inarra et al., which imply that the corresponding stochastic processes are absorbing Markov chains. The second part of the paper proposes new techniques to analyse the behaviour of matching markets. We introduce the Stable Marriage and Stable Roommates Automaton and show how the probabilistic model checking tool PRISM may be used to predict the outcomes of stochastic interactions between myopic agents. In particular, we demonstrate how one can calculate the probabilities of reaching different matchings in a decentralised market and determine the expected convergence time of the stochastic process concerned. We illustrate the usage of this technique by studying some well-known marriage and roommates instances and randomly generated instances. Copyright Springer-Verlag Berlin Heidelberg 2013

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://hdl.handle.net/10.1007/s00182-012-0352-8
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Springer in its journal International Journal of Game Theory.

    Volume (Year): 42 (2013)
    Issue (Month): 4 (November)
    Pages: 1021-1040

    as in new window
    Handle: RePEc:spr:jogath:v:42:y:2013:i:4:p:1021-1040

    Contact details of provider:
    Web page: http://link.springer.de/link/service/journals/00182/index.htm

    Order Information:
    Web: http://link.springer.de/orders.htm

    Related research

    Keywords: Stable matchings; Path to stability; Markov chain; Model checking;

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Suryapratim Banerjee & Hideo Konishi & Tayfun Sonmez, 1999. "Core in a Simple Coalition Formation Game," Boston College Working Papers in Economics 449, Boston College Department of Economics.
    2. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2008. "Stochastic Stability for Roommate Markets," Research Memorandum 010, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Bo Chen & Satoru Fujishige & Zaifu Yang, 2010. "Decentralized Market Processes to Stable Job Matchings with Competitive Salaries," KIER Working Papers 749, Kyoto University, Institute of Economic Research.
    4. James W. Boudreau, 2008. "Preference Structure and Random Paths to Stability in Matching Markets," Working papers 2008-29, University of Connecticut, Department of Economics.
    5. E. Inarra & C. Larrea & E. Molis, 2008. "Random paths to P-stability in the roommate problem," International Journal of Game Theory, Springer, vol. 36(3), pages 461-471, March.
    6. 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, vol. 36(3), pages 333-352, March.
    7. Larrea Jaurrieta, María Concepción & Iñarra García, María Elena & Molis Bañales, Elena, 2007. "The Stability of the Roommate Problem Revisited," IKERLANAK 2007-30, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    8. László Á. Kóczy & Luc Lauwers, 2001. "The Coalition Structure Core is Accessible," Game Theory and Information 0110001, EconWPA, revised 26 Jun 2002.
    9. 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.
    10. Joana Pais & Agnes Pinter & Robert F. Veszteg, 2012. "Decentralized Matching Markets: A Laboratory Experiment," Working Papers Department of Economics 2012/08, ISEG - School of Economics and Management, Department of Economics, University of Lisbon.
    11. Blum, Yosef & Rothblum, Uriel G., 2002. ""Timing Is Everything" and Marital Bliss," Journal of Economic Theory, Elsevier, vol. 103(2), pages 429-443, April.
    12. Ma, Jinpeng, 1996. "On Randomized Matching Mechanisms," Economic Theory, Springer, vol. 8(2), pages 377-81, August.
    13. Fuhito Kojima & M. Ünver, 2008. "Random paths to pairwise stability in many-to-many matching problems: a study on market equilibration," International Journal of Game Theory, Springer, vol. 36(3), pages 473-488, March.
    14. Yang, Yi-You, 2011. "Accessible outcomes versus absorbing outcomes," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 65-70, July.
    15. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:spr:jogath:v:42:y:2013:i:4:p:1021-1040. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F Baum).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.