IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v444y2016icp397-402.html
   My bibliography  Save this article

Analysis of ground state in random bipartite matching

Author

Listed:
  • Shi, Gui-Yuan
  • Kong, Yi-Xiu
  • Liao, Hao
  • Zhang, Yi-Cheng

Abstract

Bipartite matching problems emerge in many human social phenomena. In this paper, we study the ground state of the Gale–Shapley model, which is the most popular bipartite matching model. We apply the Kuhn–Munkres algorithm to compute the numerical ground state of the model. For the first time, we obtain the number of blocking pairs which is a measure of the system instability. We also show that the number of blocking pairs formed by each person follows a geometric distribution. Furthermore, we study how the connectivity in the bipartite matching problems influences the instability of the ground state.

Suggested Citation

  • Shi, Gui-Yuan & Kong, Yi-Xiu & Liao, Hao & Zhang, Yi-Cheng, 2016. "Analysis of ground state in random bipartite matching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 397-402.
    • Handle: RePEc:eee:phsmap:v:444:y:2016:i:c:p:397-402
    DOI: 10.1016/j.physa.2015.10.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843711500850X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2015.10.005?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. Dzierzawa, Michael & Oméro, Marie-José, 2000. "Statistics of stable marriages," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 321-333.
    2. Paolo Laureti Yi-Cheng Zhang, 2003. "Matching games with partial information," Game Theory and Information 0307002, University Library of Munich, Germany.
    3. Zhang, Yi-Cheng, 2001. "Happier world with more information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 104-120.
    4. Laureti, Paolo & Zhang, Yi-Cheng, 2003. "Matching games with partial information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 49-65.
    5. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    6. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
    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. Fenoaltea, Enrico Maria & Baybusinov, Izat B. & Na, Xu & Zhang, Yi-Cheng, 2022. "A local interaction dynamic for the matching problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    2. Yi-Xiu Kong & Guang-Hui Yuan & Lei Zhou & Rui-Jie Wu & Gui-Yuan Shi, 2018. "Competition May Increase Social Utility in Bipartite Matching Problem," Complexity, Hindawi, vol. 2018, pages 1-7, November.
    3. Liu, Xiao-Lu & Liu, Jian-Guo & Yang, Kai & Guo, Qiang & Han, Jing-Ti, 2017. "Identifying online user reputation of user–object bipartite networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 508-516.

    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. Yi-Xiu Kong & Guang-Hui Yuan & Lei Zhou & Rui-Jie Wu & Gui-Yuan Shi, 2018. "Competition May Increase Social Utility in Bipartite Matching Problem," Complexity, Hindawi, vol. 2018, pages 1-7, November.
    2. Fenoaltea, Enrico Maria & Baybusinov, Izat B. & Na, Xu & Zhang, Yi-Cheng, 2022. "A local interaction dynamic for the matching problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    3. André Veski & Kaire Põder, 2018. "Zero-intelligence agents looking for a job," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 13(3), pages 615-640, October.
    4. Tilles, Paulo F.C. & Ferreira, Fernando F. & Francisco, Gerson & Pereira, Carlos de B. & Sarti, Flavia M., 2011. "A Markovian model market—Akerlof’s lemons and the asymmetry of information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2562-2570.
    5. Jiang, Zhishan & Tian, Guoqiang, 2013. "Matching with Couples: Stability and Algorithm," MPRA Paper 57936, University Library of Munich, Germany, revised Jul 2014.
    6. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    7. Tao Jia & Robert F Spivey & Boleslaw Szymanski & Gyorgy Korniss, 2015. "An Analysis of the Matching Hypothesis in Networks," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-12, June.
    8. Bettina Klaus & Flip Klijn, 2006. "Procedurally fair and stable matching," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 431-447, January.
    9. Hideo Konishi & M. Ünver, 2006. "Games of Capacity Manipulation in Hospital-intern Markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 3-24, August.
    10. Michele Lombardi & Naoki Yoshihara, 2020. "Partially-honest Nash implementation: a full characterization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 871-904, October.
    11. Hidemasa Ishii & Nariaki Nishino, 2022. "Asymptotically stable matchings and evolutionary dynamics of preference revelation games in marriage problems," Papers 2205.08079, arXiv.org.
    12. Sebastian Montano Correa, 2015. "Compulsory Social Service Matching Market for Physicians in Colombia," Documentos CEDE 12856, Universidad de los Andes, Facultad de Economía, CEDE.
    13. Roth, Alvin E. & Sotomayor, Marilda, 1996. "Stable Outcomes in Discrete and Continuous Models of Two-Sided Matching: a Unified Treatment," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 16(2), November.
    14. Jens Gudmundsson, 2014. "Sequences in Pairing Problems: A new approach to reconcile stability with strategy-proofness for elementary matching problems," 2014 Papers pgu351, Job Market Papers.
    15. Konishi, Hideo & Unver, M. Utku, 2006. "Credible group stability in many-to-many matching problems," Journal of Economic Theory, Elsevier, vol. 129(1), pages 57-80, July.
    16. 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.
    17. Bikhchandani, Sushil, 2017. "Stability with one-sided incomplete information," Journal of Economic Theory, Elsevier, vol. 168(C), pages 372-399.
    18. Coles, Peter & Shorrer, Ran, 2014. "Optimal truncation in matching markets," Games and Economic Behavior, Elsevier, vol. 87(C), pages 591-615.
    19. Vinay Ramani & K. S. Mallikarjuna Rao, 2018. "Paths to stability and uniqueness in two-sided matching markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1137-1150, November.
    20. 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.

    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:phsmap:v:444:y:2016:i:c:p:397-402. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.