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A Perfectly Robust Approach to Multiperiod Matching Problems

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  • Kotowski, Maciej

    (Harvard Kennedy School)

Abstract

Many two-sided matching situations involve multiperiod interaction. Traditional cooperative solutions, such as stability and the core, often identify unintuitive outcomes (or are empty) when applied to such markets. As an alternative, this study proposes the criterion of perfect alpha-stability. An outcome is perfect alpha-stable if no coalition prefers an alternative assignment in any period that is superior for all plausible market continuations. Behaviorally, the solution combines foresight about the future and a robust evaluation of contemporaneous outcomes. A perfect alpha-stable matching exists, even when preferences exhibit inter-temporal complementarities. A stronger solution, the perfect alpha-core, is also investigated. Extensions to markets with arrivals and departures, transferable utility, and many-to-one assignments are proposed.

Suggested Citation

  • Kotowski, Maciej, 2019. "A Perfectly Robust Approach to Multiperiod Matching Problems," Working Paper Series rwp19-016, Harvard University, John F. Kennedy School of Government.
    • Handle: RePEc:ecl:harjfk:rwp19-016
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    File URL: https://research.hks.harvard.edu/publications/getFile.aspx?Id=2790
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    References listed on IDEAS

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    Cited by:

    1. Laura Doval & Pablo Schenone, 2024. "Consistent Conjectures in Dynamic Matching Markets," Papers 2407.04857, arXiv.org, revised Oct 2024.
    2. Haeringer, Guillaume & Iehlé, Vincent, 2021. "Gradual college admission," Journal of Economic Theory, Elsevier, vol. 198(C).
    3. Liu, Ce & Ali, S. Nageeb, 2019. "Conventions and Coalitions in Repeated Games," Working Papers 2019-8, Michigan State University, Department of Economics.
    4. Morimitsu Kurino, 2020. "Credibility, efficiency, and stability: a theory of dynamic matching markets," The Japanese Economic Review, Springer, vol. 71(1), pages 135-165, January.
    5. Liu, Ce, 2023. "Stability in repeated matching markets," Theoretical Economics, Econometric Society, vol. 18(4), November.
    6. Umut Dur & Thayer Morrill & William Phan, 2024. "Partitionable choice functions and stability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(2), pages 359-375, September.
    7. Ce Liu, 2020. "Stability in Repeated Matching Markets," Papers 2007.03794, arXiv.org, revised Mar 2021.
    8. Doval, Laura, 2022. "Dynamically stable matching," Theoretical Economics, Econometric Society, vol. 17(2), May.
    9. Vincent Iehlé, 2016. "Gradual College Admisssion," Post-Print halshs-02367006, HAL.

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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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