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The Roommate Problem is More Stable than You Think

Author

Listed:
  • Pierre-André Chiappori

    (Department of Economics (Columbia))

  • Alfred Galichon

    (Département d'économie (ECON))

  • Bernard Salanié

    (Department of Economics (Columbia))

Abstract

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, 2012. "The Roommate Problem is More Stable than You Think," Sciences Po publications info:hdl:2441/3sd5loegec9, Sciences Po.
    • Handle: RePEc:spo:wpmain:info:hdl:2441/3sd5loegec9d3o795888da61tp
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Edoardo Ciscato & Alfred Galichon & Marion Goussé, 2020. "Like Attract Like? A Structural Comparison of Homogamy across Same-Sex and Different-Sex Households," Journal of Political Economy, University of Chicago Press, vol. 128(2), pages 740-781.
    2. à ureo de Paula & Seth Richards†Shubik & Elie Tamer, 2018. "Identifying Preferences in Networks With Bounded Degree," Econometrica, Econometric Society, vol. 86(1), pages 263-288, January.
    3. repec:hal:spmain:info:hdl:2441/10gq8jbaid85sben727o7nd22a is not listed on IDEAS
    4. David Pérez-Castrillo & Marilda Sotomayor, 2023. "Constrained-optimal tradewise-stable outcomes in the one-sided assignment game: a solution concept weaker than the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(3), pages 963-994, October.
    5. repec:hal:spmain:info:hdl:2441/38n7438p68vmqd9om4bjj6l4c is not listed on IDEAS
    6. Andersson, T. & Erlanson, A. & Gudmundsson, J. & Habis, H. & Ingebretsen Carlson, J. & Kratz, J., 2014. "A method for finding the maximal set in excess demand," Economics Letters, Elsevier, vol. 125(1), pages 18-20.
    7. Jeremy T. Fox & David H. Hsu & Chenyu Yang, 2012. "Unobserved Heterogeneity in Matching Games with an Application to Venture Capital," NBER Working Papers 18168, National Bureau of Economic Research, Inc.
    8. Alfred Galichon & Bernard Salanié, 2022. "Cupid’s Invisible Hand: Social Surplus and Identification in Matching Models [An Empirical Model of the Medical Match]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(5), pages 2600-2629.
    9. Bernard Salanié & Alfred Galichon, 2012. "Cupid's Invisible Hand: Social Surplus and Identification in Matching Models," Working Papers hal-01053710, HAL.
    10. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0c7apsi is not listed on IDEAS
    11. Jens Gudmundsson, 2014. "Sequences in Pairing Problems: A new approach to reconcile stability with strategy-proofness for elementary matching problems," 2014 Papers pgu351, Job Market Papers.
    12. Elizabeth Baldwin & Paul Klemperer, 2019. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities," Econometrica, Econometric Society, vol. 87(3), pages 867-932, May.
    13. 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.
    14. Akiyoshi Shioura, 2017. "On the Partnership formation problem," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 2(1), pages 105-140, December.
    15. Pęski, Marcin, 2017. "Large roommate problem with non-transferable random utility," Journal of Economic Theory, Elsevier, vol. 168(C), pages 432-471.
    16. Gudmundsson, Jens, 2013. "Cycles and Third-Party Payments in the Partnership Formation Problem," Working Papers 2013:16, Lund University, Department of Economics.
    17. Edoardo Ciscato & Alfred Galichon & Marion Goussé, 2020. "Like Attract Like? A Structural Comparison of Homogamy across Same-Sex and Different-Sex Households," Journal of Political Economy, University of Chicago Press, vol. 128(2), pages 740-781.
    18. Ahmet Alkan & Alparslan Tuncay, 2014. "Pairing Games and Markets," Working Papers 2014.48, Fondazione Eni Enrico Mattei.
    19. Xinyang Wang, 2020. "Cooperation in Small Groups -- an Optimal Transport Approach," Papers 2005.11244, arXiv.org.
    20. Tommaso Porzio, 2016. "Distance to the Technology Frontier and the Allocation of Talent," 2016 Meeting Papers 569, Society for Economic Dynamics.
    21. Manjunath, Vikram, 2016. "Fractional matching markets," Games and Economic Behavior, Elsevier, vol. 100(C), pages 321-336.
    22. Hakan İnal, 2014. "A Generalization of the Lone Wolf Theorem," Metroeconomica, Wiley Blackwell, vol. 65(4), pages 541-547, November.

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    More about this item

    Keywords

    Matching; Roommate Problem; Stability;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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