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The marriage problem: From the bar of appointments to the agency

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  • Lage-Castellanos, Alejandro
  • Mulet, Roberto

Abstract

We study the stable marriage problem from different points of view. We proposed a microscopic dynamic that led the system to a stationary state that we are able to characterize analytically. Then, we derive a thermodynamical description of the Nash equilibrium states of the system that agree very well with the results of Monte Carlo simulations. Finally, through large-scale numerical simulations we compare the global optimum of the society with the stable marriage of lower energy. We showed that both states are strongly correlated and that the selfish attitude results in a benefit for most of the practitioners belonging to blocking pairs in the global optimum of the society.

Suggested Citation

  • Lage-Castellanos, Alejandro & Mulet, Roberto, 2006. "The marriage problem: From the bar of appointments to the agency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 389-402.
    • Handle: RePEc:eee:phsmap:v:364:y:2006:i:c:p:389-402
    DOI: 10.1016/j.physa.2005.08.042
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    Cited by:

    1. Enrico Maria Fenoaltea & Izat B. Baybusinov & Jianyang Zhao & Lei Zhou & Yi-Cheng Zhang, 2021. "The Stable Marriage Problem: an Interdisciplinary Review from the Physicist's Perspective," Papers 2103.11458, arXiv.org.
    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. Medo, Matúš & Zhang, Yi-Cheng, 2008. "Market model with heterogeneous buyers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2889-2908.
    4. 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.

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