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The Roommate Problem - Is More Stable Than You Think

Author

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

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    Citations

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    Cited by:

    1. 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.
    2. repec:hal:spmain:info:hdl:2441/38n7438p68vmqd9om4bjj6l4c is not listed on IDEAS
    3. 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.
    4. repec:spo:wpmain:info:hdl:2441/38n7438p68vmqd9om4bjj6l4c is not listed on IDEAS
    5. Bernard Salanié & Alfred Galichon, 2012. "Cupid's Invisible Hand: Social Surplus and Identification in Matching Models," Working Papers hal-01053710, HAL.
    6. 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.
    7. 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.
    8. 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.
    9. Pęski, Marcin, 2017. "Large roommate problem with non-transferable random utility," Journal of Economic Theory, Elsevier, vol. 168(C), pages 432-471.
    10. Gudmundsson, Jens, 2013. "Cycles and Third-Party Payments in the Partnership Formation Problem," Working Papers 2013:16, Lund University, Department of Economics.
    11. 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.
    12. 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.
    13. Gudmundsson , Jens, 2014. "Sequences in Pairing Problems: A New Approach to Reconcile Stability with Strategy-Proofness for Elementary Matching Problems," Working Papers 2014:40, Lund University, Department of Economics.
    14. Alfred Galichon & Bernard Salanié, 2022. "Cupid’s Invisible Hand: Social Surplus and Identification in Matching Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(5), pages 2600-2629.
    15. Xinyang Wang, 2020. "Cooperation in Small Groups -- an Optimal Transport Approach," Papers 2005.11244, arXiv.org.
    16. Manjunath, Vikram, 2016. "Fractional matching markets," Games and Economic Behavior, Elsevier, vol. 100(C), pages 321-336.
    17. Hakan İnal, 2014. "A Generalization of the Lone Wolf Theorem," Metroeconomica, Wiley Blackwell, vol. 65(4), pages 541-547, November.
    18. 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.
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    20. 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.
    21. Ahmet Alkan & Alparslan Tuncay, 2014. "Pairing Games and Markets," Working Papers 2014.48, Fondazione Eni Enrico Mattei.
    22. Tommaso Porzio, 2016. "Distance to the Technology Frontier and the Allocation of Talent," 2016 Meeting Papers 569, Society for Economic Dynamics.

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    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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