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Robust minimal instability of the top trading cycles mechanism

Author

Listed:
  • Battal Dogan

    (University of Bristol)

  • Lars Ehlers

    (Université de Montréal)

Abstract

In the context of priority-based resource allocation, we formulate methods to compare assignments in terms of their stability as binary relations (on the set of possible assignments) that depend on the preference and the priority profile. We introduce three basic properties, stability preferred, separability, and consistency, that a reasonable stability comparison should satisfy. We show that, for any stability comparison satisfying the three properties, the top trading cycles (TTC) mechanism is minimally unstable among efficient and strategy-proof mechanisms in one-to-one matching. An important consequence is the robustness of a recent result by Abdulkadiroglu et al. (2019), which uses a particular stability comparison method where an assignment is more stable than another assignment if the set of blocking pairs in the former assignment is a subset of the set of blocking pairs in the latter assignment. Our unifying approach covers basically all natural comparison methods and it includes many cardinal stability comparison methods as special cases.

Suggested Citation

  • Battal Dogan & Lars Ehlers, 2020. "Robust minimal instability of the top trading cycles mechanism," Cahiers de recherche 2020-01, Universite de Montreal, Departement de sciences economiques.
    • Handle: RePEc:mtl:montde:2020-01
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    File URL: http://hdl.handle.net/1866/23125
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    References listed on IDEAS

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    1. Rustamdjan Hakimov & Onur Kesten, 2018. "The Equitable Top Trading Cycles Mechanism For School Choice," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(4), pages 2219-2258, November.
    2. Lars-Gunnar Svensson, 1999. "Strategy-proof allocation of indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 557-567.
    3. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    4. Morrill, Thayer, 2015. "Making just school assignments," Games and Economic Behavior, Elsevier, vol. 92(C), pages 18-27.
    5. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    6. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 75-83.
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    Citations

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    Cited by:

    1. Ata Atay & Ana Mauleon & Vincent Vannetelbosch, 2022. "Limited Farsightedness in Priority-Based Matching," Papers 2212.07427, arXiv.org.
    2. Estelle Cantillon & Li Chen & Juan S. Pereyra, 2022. "Respecting priorities versus respecting preferences in school choice: When is there a trade-off?," Papers 2212.02881, arXiv.org, revised Sep 2024.
    3. Rodríguez-Álvarez, Carmelo & Romero-Medina, Antonio, 2024. "School choice with transferable student characteristics," Games and Economic Behavior, Elsevier, vol. 143(C), pages 103-124.
    4. Dur, Umut & Paiement, Scott, 2024. "A characterization of the top trading cycles mechanism for the school choice problem," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 93-100.
    5. Battal Dogan & Lars Ehlers, 2020. "Blocking pairs versus blocking students: Stability comparisons in school choice," Cahiers de recherche 2020-02, Universite de Montreal, Departement de sciences economiques.
    6. Somouaoga Bonkoungou & Alexander Nesterov, 2020. "Reforms meet fairness concerns in school and college admissions," Papers 2009.05245, arXiv.org, revised Sep 2024.
    7. Siwei Chen & Yajing Chen & Chia‐Ling Hsu, 2023. "New axioms for top trading cycles," Bulletin of Economic Research, Wiley Blackwell, vol. 75(4), pages 1064-1077, October.
    8. Afacan, Mustafa Oğuz & Hu, Gaoji & Li, Jiangtao, 2024. "Housing markets since Shapley and Scarf," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    9. Estelle Cantillon & Li Chen & Juan Sebastian Pereyra Barreiro, 2022. "Respecting priorities versus respecting preferences in school choice: When is there a trade-off ?," Working Papers ECARES 2022-39, ULB -- Universite Libre de Bruxelles.
    10. Pierre Callataÿ & Ana Mauleon & Vincent Vannetelbosch, 2024. "Minimal farsighted instability," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 493-523, June.
    11. Afacan, Mustafa Oğuz & Dur, Umut, 2024. "Rawlsian Matching," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 101-106.
    12. Mustafa Oğuz Afacan & Umut Dur, 2023. "Strategy‐proof size improvement: is it possible?," Scandinavian Journal of Economics, Wiley Blackwell, vol. 125(2), pages 321-338, April.

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    More about this item

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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