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Gale-Shapley Stable Marriage Problem Revisited: Strategic Issues and Applications

Author

Listed:
  • Chung-Piaw Teo

    () (Department of Decision Sciences, Faculty of Business Administration, National University of Singapore, FBA 1-15 Law Link, Singapore 117591)

  • Jay Sethuraman

    () (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Wee-Peng Tan

    (Department of Decision Sciences, Faculty of Business Administration, National University of Singapore, FBA 1-15 Law Link, Singapore 117591)

Abstract

We study strategic issues in the Gale-Shapley stable marriage model. In the first part of the paper, we derive the optimal cheating strategy and show that it is not always possible for a woman to recover her women-optimal stable partner from the men-optimal stable matching mechanism when she can only cheat by permuting her preferences. In fact, we show, using simulation, that the chances that a woman can benefit from cheating are slim. In the second part of the paper, we consider a two-sided matching market found in Singapore. We study the matching mechanism used by the Ministry of Education (MOE) in the placement of primary six students in secondary schools, and discuss why the current method has limited success in accommodating the preferences of the students, and the specific needs of the schools (in terms of the "mix" of admitted students). Using insights from the first part of the paper, we show that stable matching mechanisms are more appropriate in this matching market and explain why the strategic behavior of the students need not be a major concern.

Suggested Citation

  • Chung-Piaw Teo & Jay Sethuraman & Wee-Peng Tan, 2001. "Gale-Shapley Stable Marriage Problem Revisited: Strategic Issues and Applications," Management Science, INFORMS, vol. 47(9), pages 1252-1267, September.
  • Handle: RePEc:inm:ormnsc:v:47:y:2001:i:9:p:1252-1267
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    File URL: http://dx.doi.org/10.1287/mnsc.47.9.1252.9784
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    References listed on IDEAS

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    1. Alvin E. Roth & Uriel G. Rothblum, 1999. "Truncation Strategies in Matching Markets--In Search of Advice for Participants," Econometrica, Econometric Society, vol. 67(1), pages 21-44, January.
    2. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    3. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    4. Tadenuma, Koichi & Toda, Manabu, 1998. "Implementable stable solutions to pure matching problems," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 121-132, March.
    5. Kara, Tarik & Sonmez, Tayfun, 1996. "Nash Implementation of Matching Rules," Journal of Economic Theory, Elsevier, vol. 68(2), pages 425-439, February.
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    Citations

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    Cited by:

    1. Boudreau, James W., 2010. "Stratification and growth in agent-based matching markets," Journal of Economic Behavior & Organization, Elsevier, vol. 75(2), pages 168-179, August.
    2. Egbert, Henrik & Neumann, Thomas & Rasmus, Anke, 2014. "Matchingtools und Matchingprozesse im Kontext von Junior und Senior Entrepreneuren
      [Matching Tools and Processes in the Context of Junior and Senior Entrepreneurship]
      ," MPRA Paper 54829, University Library of Munich, Germany.
    3. Kóczy Á., László, 2010. "A magyarországi felvételi rendszerek sajátosságai
      [Specific features of Hungarys system of school and university admissions]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(2), pages 142-164.
    4. Peng, Zixuan & Shan, Wenxuan & Guan, Feng & Yu, Bin, 2016. "Stable vessel-cargo matching in dry bulk shipping market with price game mechanism," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 95(C), pages 76-94.
    5. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1921-1947, September.
    6. James W. Boudreau & Vicki Knoblauch, 2010. "Marriage Matching and Intercorrelation of Preferences," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 12(3), pages 587-602, June.
    7. Ergin, Haluk & Sonmez, Tayfun, 2006. "Games of school choice under the Boston mechanism," Journal of Public Economics, Elsevier, vol. 90(1-2), pages 215-237, January.
    8. repec:ebl:ecbull:v:3:y:2008:i:67:p:1-12 is not listed on IDEAS
    9. Kóczy Á., László, 2009. "Központi felvételi rendszerek. Taktikázás és stabilitás
      [Central admission systems. Stratagems and stability]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(5), pages 422-442.
    10. James Boudreau & Vicki Knoblauch, 2013. "Preferences and the price of stability in matching markets," Theory and Decision, Springer, vol. 74(4), pages 565-589, April.
    11. Klaus, Bettina & Klijn, Flip, 2016. "Equilibria of deferred acceptance with complete lists," Economics Letters, Elsevier, vol. 144(C), pages 98-101.
    12. James Boudreau, 2008. "Preference Structure and Random Paths to Stability in Matching Markets," Economics Bulletin, AccessEcon, vol. 3(67), pages 1-12.
    13. Hai-Liu Shi & Ying-Ming Wang & Sheng-Qun Chen & Yi-Xin Lan, 2017. "An approach to two-sided M&A fits based on a cross-efficiency evaluation with contrasting attitudes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(1), pages 41-52, January.
    14. Péter Biró & Sofya Kiselgof, 2015. "College admissions with stable score-limits," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 727-741, December.

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