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The roommates problem revisited


  • Morrill, Thayer


One of the oldest matching problems is Gale and Shapley's (1962) [8] "roommates problem": is there a stable way to assign 2N students into N roommate pairs? Unlike the classic marriage problem or college admissions problem, there need not exist a stable solution to the roommates problem. However, stability ignores the key physical constraint that roommates require a room and is therefore too restrictive. This motivates a new matching problem: matching agents subject to an initial assignment. A particularly important example is kidney exchange where after an assignment has been made, subsequent tests may determine that a patient and donor are incompatible. This paper introduces an efficient algorithm for finding a Pareto improvement starting from any status quo roommates assignment.

Suggested Citation

  • Morrill, Thayer, 2010. "The roommates problem revisited," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1739-1756, September.
  • Handle: RePEc:eee:jetheo:v:145:y:2010:i:5:p:1739-1756

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    References listed on IDEAS

    1. Tayfun Sönmez & Alvin E. Roth & M. Utku Ünver, 2007. "Efficient Kidney Exchange: Coincidence of Wants in Markets with Compatibility-Based Preferences," American Economic Review, American Economic Association, vol. 97(3), pages 828-851, June.
    2. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    3. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May.
    4. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
    5. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
    6. Parag A. Pathak & Tayfun Sonmez, 2008. "Leveling the Playing Field: Sincere and Sophisticated Players in the Boston Mechanism," American Economic Review, American Economic Association, vol. 98(4), pages 1636-1652, September.
    7. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    8. Alvin E. Roth & Tayfun Sönmez, 2005. "A Kidney Exchange Clearinghouse in New England," American Economic Review, American Economic Association, vol. 95(2), pages 376-380, May.
    9. Aytek Erdil & Haluk Ergin, 2008. "What's the Matter with Tie-Breaking? Improving Efficiency in School Choice," American Economic Review, American Economic Association, vol. 98(3), pages 669-689, June.
    10. S. Illeris & G. Akehurst, 2001. "Introduction," The Service Industries Journal, Taylor & Francis Journals, vol. 21(1), pages 1-4, January.
    11. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    12. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, vol. 99(5), pages 1954-1978, December.
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    Cited by:

    1. 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.
    2. Aziz, Haris & Brandt, Felix & Harrenstein, Paul, 2013. "Pareto optimality in coalition formation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 562-581.
    3. Hakan İnal, 2014. "A Generalization of the Lone Wolf Theorem," Metroeconomica, Wiley Blackwell, vol. 65(4), pages 541-547, November.
    4. Peter Biro & Elena Iñarra & Elena Molis, 2014. "A new solution for the roommate problem. The Q-stable matchings," ThE Papers 14/04, Department of Economic Theory and Economic History of the University of Granada..
    5. Biró, Péter & Iñarra, Elena & Molis, Elena, 2016. "A new solution concept for the roommate problem: Q-stable matchings," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 74-82.


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