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Analysis of ground state in random bipartite matching

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

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    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. 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.

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