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Stability and strategy-proofness for matching with constraints: a necessary and sufficient condition

Author

Listed:
  • Kamada, Yuichiro

    (Haas School of Business, University of California, Berkeley)

  • Kojima, Fuhito

    (Department of Economics, Stanford University)

Abstract

Distributional constraints are common features in many real matching markets, such as medical residency matching, school admissions, and teacher assignment. We develop a general theory of matching mechanisms under distributional constraints. We identify the necessary and sufficient condition on the constraint structure for the existence of a mechanism that is stable and strategy-proof for the individuals. Our proof exploits a connection between a matching problem under distributional constraints and a matching problem with contracts.

Suggested Citation

  • Kamada, Yuichiro & Kojima, Fuhito, 2018. "Stability and strategy-proofness for matching with constraints: a necessary and sufficient condition," Theoretical Economics, Econometric Society, vol. 13(2), May.
    • Handle: RePEc:the:publsh:2717
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    References listed on IDEAS

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    Cited by:

    1. Yannai A. Gonczarowski & Lior Kovalio & Noam Nisan & Assaf Romm, 2019. "Matching for the Israeli "Mechinot" Gap-Year Programs: Handling Rich Diversity Requirements," Papers 1905.00364, arXiv.org, revised Aug 2020.
    2. Ayoade, Nickesha & Pápai, Szilvia, 2023. "School choice with preference rank classes," Games and Economic Behavior, Elsevier, vol. 137(C), pages 317-341.
    3. Avataneo, Michelle & Turhan, Bertan, 2021. "Slot-specific priorities with capacity transfers," Games and Economic Behavior, Elsevier, vol. 129(C), pages 536-548.
    4. Battal Dou{g}an & Kenzo Imamura & M. Bumin Yenmez, 2022. "Market Design with Deferred Acceptance: A Recipe for Policymaking," Papers 2209.06777, arXiv.org.
    5. Tomoeda, Kentaro, 2018. "Finding a stable matching under type-specific minimum quotas," Journal of Economic Theory, Elsevier, vol. 176(C), pages 81-117.
    6. Haris Aziz & Serge Gaspers & Zhaohong Sun & Toby Walsh, 2020. "From Matching with Diversity Constraints to Matching with Regional Quotas," Papers 2002.06748, arXiv.org.
    7. Reischmann, Tobias & Klein, Thilo & Giegerich, Sven, 2021. "An iterative deferred acceptance mechanism for decentralized, fast and fair childcare assignment," ZEW Discussion Papers 21-095, ZEW - Leibniz Centre for European Economic Research.
    8. Muhammad Maaz & Anastasios Papanastasiou, 2020. "Matching with Compatibility Constraints: The Case of the Canadian Medical Residency Match," Department of Economics Working Papers 2020-15, McMaster University.
    9. Mackenzie, Andrew & Zhou, Yu, 2022. "Menu mechanisms," Journal of Economic Theory, Elsevier, vol. 204(C).
    10. Yuichiro Kamada & Fuhito Kojima, 2020. "Accommodating various policy goals in matching with constraints," The Japanese Economic Review, Springer, vol. 71(1), pages 101-133, January.
    11. Haris Aziz & Anton Baychkov & Peter Biro, 2021. "Cutoff stability under distributional constraints with an application to summer internship matching," Papers 2102.02931, arXiv.org, revised Oct 2023.
    12. Avinatan Hassidim & Assaf Romm & Ran I. Shorrer, 2021. "The Limits of Incentives in Economic Matching Procedures," Management Science, INFORMS, vol. 67(2), pages 951-963, February.
    13. Oguzhan Celebi, 2023. "Diversity Preferences, Affirmative Action and Choice Rules," Papers 2310.14442, arXiv.org.
    14. Hafalir, Isa E. & Kojima, Fuhito & Yenmez, M. Bumin, 2022. "Interdistrict school choice: A theory of student assignment," Journal of Economic Theory, Elsevier, vol. 201(C).
    15. Aygün, Orhan & Turhan, Bertan, 2019. "Matching with Generalized Lexicographic Choice Rules," ISU General Staff Papers 20191101070000, Iowa State University, Department of Economics.
    16. Jagadeesan, Ravi, 2018. "Lone wolves in infinite, discrete matching markets," Games and Economic Behavior, Elsevier, vol. 108(C), pages 275-286.
    17. Yao Cheng & Zaifu Yang, "undated". "Stable Matching Mechanisms under Distributional Constraints," Discussion Papers 23/03, Department of Economics, University of York.
    18. Tobias Reischmann & Thilo Klein & Sven Giegerich, 2021. "A deferred acceptance mechanism for decentralized, fast, and fair childcare assignment," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 6(1), pages 59-100, December.
    19. Yao Cheng & Zaifu Yang, 2023. "Stable Matching Mechanisms under Distributional Constraints," Discussion Papers 23/05, Department of Economics, University of York.
    20. Devansh Jalota & Michael Ostrovsky & Marco Pavone, 2022. "Matching with Transfers under Distributional Constraints," Papers 2202.05232, arXiv.org, revised Apr 2022.
    21. Orhan Aygun & Bertan Turhan, 2020. "Designing Direct Matching Mechanism for India with Comprehensive Affirmative Action," Papers 2004.13264, arXiv.org, revised Dec 2021.

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    More about this item

    Keywords

    Matching with constraints; medical residency matching; school choice; stability; strategy-proofness; matching with contracts; hierarchy;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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