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The Roommate Problem - Is More Stable Than You Think


  • Pierre-André Chiappori
  • Alfred Galichon
  • Bernard Salanié


Stable matchings may fail to exist in the roommate matching problem, both when utility is transferable and when it is not. We show that when utility is transferable, the existence of a stable matching is restored when there is an even number of individuals of indistinguishable characteristics and tastes (types). As a consequence, when the number of individuals of any given type is large enough there always exist "quasi-stable" matchings: a stable matching can be restored with minimal policy intervention. Our results build on an analogy with an associated bipartite problem; it follows that the tools crafted in empirical studies of the marriage problem can easily be adapted to the roommate problem.

Suggested Citation

  • Pierre-André Chiappori & Alfred Galichon & Bernard Salanié, 2014. "The Roommate Problem - Is More Stable Than You Think," CESifo Working Paper Series 4676, CESifo Group Munich.
  • Handle: RePEc:ces:ceswps:_4676

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    References listed on IDEAS

    1. Eugene Choo & Aloysius Siow, 2006. "Who Marries Whom and Why," Journal of Political Economy, University of Chicago Press, vol. 114(1), pages 175-201, February.
    2. Abhijit Banerjee & Esther Duflo & Maitreesh Ghatak & Jeanne Lafortune, 2013. "Marry for What? Caste and Mate Selection in Modern India," American Economic Journal: Microeconomics, American Economic Association, vol. 5(2), pages 33-72, May.
    3. Pierre-André Chiappori & Sonia Oreffice & Climent Quintana, 2009. "Fatter Attraction: Anthropometric and Socioeconomic Characteristics in the Marriage Market," Working Papers 2009-34, FEDEA.
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    6. Talman, Dolf & Yang, Zaifu, 2011. "A model of partnership formation," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 206-212, March.
    7. Bettina Klaus & Flip Klijn, 2007. "Smith and Rawls Share a Room," UFAE and IAE Working Papers 706.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    8. Gunter J. Hitsch & Ali Hortaçsu & Dan Ariely, 2010. "Matching and Sorting in Online Dating," American Economic Review, American Economic Association, vol. 100(1), pages 130-163, March.
    9. Weyl, E. Glen & White, Alexander & Azevedo, Eduardo M., 2013. "Walrasian equilibrium in large, quasi-linear markets," Theoretical Economics, Econometric Society, vol. 8(2), May.
    10. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-846, July-Aug..
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    12. Bettina Klaus & Alexandru Nichifor, 2010. "Consistency in one-sided assignment problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(3), pages 415-433, September.
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    Cited by:

    1. Pęski, Marcin, 2017. "Large roommate problem with non-transferable random utility," Journal of Economic Theory, Elsevier, vol. 168(C), pages 432-471.
    2. Andersson, Tommy & Gudmundsson, Jens & Talman, Dolf & Yang, Zaifu, 2014. "A competitive partnership formation process," Games and Economic Behavior, Elsevier, vol. 86(C), pages 165-177.
    3. Manjunath, Vikram, 2016. "Fractional matching markets," Games and Economic Behavior, Elsevier, vol. 100(C), pages 321-336.
    4. Hakan İnal, 2014. "A Generalization of the Lone Wolf Theorem," Metroeconomica, Wiley Blackwell, vol. 65(4), pages 541-547, November.
    5. Tommaso Porzio, 2016. "Distance to the Technology Frontier and the Allocation of Talent," 2016 Meeting Papers 569, Society for Economic Dynamics.

    More about this item

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • J12 - Labor and Demographic Economics - - Demographic Economics - - - Marriage; Marital Dissolution; Family Structure


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