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The Stable Marriage Problem: an Interdisciplinary Review from the Physicist's Perspective

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  • Enrico Maria Fenoaltea
  • Izat B. Baybusinov
  • Jianyang Zhao
  • Lei Zhou
  • Yi-Cheng Zhang

Abstract

We present a fascinating model that has lately caught attention among physicists working in complexity related fields. Though it originated from mathematics and later from economics, the model is very enlightening in many aspects that we shall highlight in this review. It is called The Stable Marriage Problem (though the marriage metaphor can be generalized to many other contexts), and it consists of matching men and women, considering preference-lists where individuals express their preference over the members of the opposite gender. This problem appeared for the first time in 1962 in the seminal paper of Gale and Shapley and has aroused interest in many fields of science, including economics, game theory, computer science, etc. Recently it has also attracted many physicists who, using the powerful tools of statistical mechanics, have also approached it as an optimization problem. Here we present a complete overview of the Stable Marriage Problem emphasizing its multidisciplinary aspect, and reviewing the key results in the disciplines that it has influenced most. We focus, in particular, in the old and recent results achieved by physicists, finally introducing two new promising models inspired by the philosophy of the Stable Marriage Problem. Moreover, we present an innovative reinterpretation of the problem, useful to highlight the revolutionary role of information in the contemporary economy.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2103.11458
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    References listed on IDEAS

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    Cited by:

    1. Gao, Fujuan & Fenoaltea, Enrico Maria & Zhang, Yi-Cheng, 2023. "Market failure in a new model of platform design with partially informed consumers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).
    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. Meng, Fanyuan & Zhu, Jiadong & Yao, Yuheng & Fenoaltea, Enrico Maria & Xie, Yubo & Yang, Pingle & Liu, Run-Ran & Zhang, Jianlin, 2023. "Disagreement and fragmentation in growing groups," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    4. Mehran Farzadmehr & Valentin Carlan & Thierry Vanelslander, 2023. "Contemporary challenges and AI solutions in port operations: applying Gale–Shapley algorithm to find best matches," Journal of Shipping and Trade, Springer, vol. 8(1), pages 1-44, December.
    5. Marco LiCalzi, 2022. "Bipartite choices," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(2), pages 551-568, December.
    6. Izat B. Baybusinov & Enrico Maria Fenoaltea & Yi-Cheng Zhang, 2022. "Negotiation problem," Papers 2201.12619, arXiv.org.
    7. Baybusinov, Izat B. & Fenoaltea, Enrico Maria & Zhang, Yi-Cheng, 2022. "Negotiation problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).

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