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The roommate problem with externalities

Author

Listed:
  • José Luis Contreras

    (National Productivity Commission)

  • Juan Pablo Torres-Martínez

    (University of Chile)

Abstract

This paper extends the roommate problem to include externalities, allowing preferences for a partner to depend on the situation of others. Stability concepts for matchings and partitions of the set of agents are proposed and characterized, conditional on all agents having prudent expectations about other agents’ reactions to deviations. We prove that any roommate problem with externalities has a stable partition and that a stable matching exists if there is a stable partition without odd rings. These results allow us to find restrictions on the space of preferences ensuring the existence of a stable matching. We also show that some classical properties are lost in the presence of externalities: the existence of paths to stability from any unstable matching, the coincidence of the core with the set of stable matchings, and the invariance of the set of agents who are alone in a stable matching.

Suggested Citation

  • José Luis Contreras & Juan Pablo Torres-Martínez, 2021. "The roommate problem with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 149-165, March.
    • Handle: RePEc:spr:jogath:v:50:y:2021:i:1:d:10.1007_s00182-020-00743-z
    DOI: 10.1007/s00182-020-00743-z
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    References listed on IDEAS

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    1. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
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    Cited by:

    1. Piazza, Adriana & Torres-Martínez, Juan Pablo, 2024. "Coalitional stability in matching problems with externalities and random preferences," Games and Economic Behavior, Elsevier, vol. 143(C), pages 321-339.
    2. Hong, Miho & Park, Jaeok, 2022. "Core and top trading cycles in a market with indivisible goods and externalities," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    3. Fonseca-Mairena, María Haydée & Triossi, Matteo, 2022. "Incentives and implementation in allocation problems with externalities," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    4. Fonseca-Mairena, María Haydée & Triossi, Matteo, 2023. "Coalition formation problems with externalities," Economics Letters, Elsevier, vol. 226(C).

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    More about this item

    Keywords

    Roommate problems; Externalities; Stable matching; Stable partition;
    All these keywords.

    JEL classification:

    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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