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Designing matching mechanisms under constraints: An approach from discrete convex analysis

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  • Kojima, Fuhito
  • Tamura, Akihisa
  • Yokoo, Makoto

Abstract

We consider two-sided matching problems where agents on one side of the market (hospitals) are required to satisfy certain distributional constraints. We show that when the preferences and constraints of the hospitals can be represented by an M♮-concave function, (i) the generalized Deferred Acceptance (DA) mechanism is strategyproof for doctors, (ii) it produces the doctor-optimal stable matching, and (iii) its time complexity is proportional to the square of the number of possible contracts. Furthermore, we provide sufficient conditions under which the generalized DA mechanism satisfies these desirable properties. These conditions are applicable to various existing works and enable new applications as well, thereby providing a recipe for developing desirable mechanisms in practice.

Suggested Citation

  • Kojima, Fuhito & Tamura, Akihisa & Yokoo, Makoto, 2018. "Designing matching mechanisms under constraints: An approach from discrete convex analysis," Journal of Economic Theory, Elsevier, vol. 176(C), pages 803-833.
    • Handle: RePEc:eee:jetheo:v:176:y:2018:i:c:p:803-833
    DOI: 10.1016/j.jet.2018.05.004
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    Cited by:

    1. 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.
    2. Julien Combe & Umut Mert Dur & Olivier Tercieux & Camille Terrier & M. Utku Ünver, 2022. "Market Design for Distributional Objectives in (Re)assignment: An Application to Improve the Distribution of Teachers in Schools," Boston College Working Papers in Economics 1050, Boston College Department of Economics.
    3. Imamura, Kenzo & Kawase, Yasushi, 2024. "Efficient matching under general constraints," Games and Economic Behavior, Elsevier, vol. 145(C), pages 197-207.
    4. Aygün, Orhan & Turhan, Bertan, 2020. "Dynamic reserves in matching markets," Journal of Economic Theory, Elsevier, vol. 188(C).
    5. Koji Yokote & Isa E. Hafalir & Fuhito Kojima & M. Bumin Yenmez, 2023. "Rationalizing Path-Independent Choice Rules," Papers 2303.00892, arXiv.org, revised May 2024.
    6. Noda, Shunya, 2023. "A planner-optimal matching mechanism and its incentive compatibility in a restricted domain," Games and Economic Behavior, Elsevier, vol. 141(C), pages 364-379.
    7. Aziz, Haris & Brandl, Florian, 2022. "The vigilant eating rule: A general approach for probabilistic economic design with constraints," Games and Economic Behavior, Elsevier, vol. 135(C), pages 168-187.
    8. Julien Combe, 2023. "Reallocation with priorities and minimal envy mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 551-584, August.
    9. Goko, Hiromichi & Igarashi, Ayumi & Kawase, Yasushi & Makino, Kazuhisa & Sumita, Hanna & Tamura, Akihisa & Yokoi, Yu & Yokoo, Makoto, 2024. "A fair and truthful mechanism with limited subsidy," Games and Economic Behavior, Elsevier, vol. 144(C), pages 49-70.
    10. Tayfun Sönmez & M. Bumin Yenmez, 2019. "Affirmative Action with Overlapping Reserves," Boston College Working Papers in Economics 990, Boston College Department of Economics, revised 15 Jan 2020.
    11. Yokote, Koji, 2021. "Consistency of the doctor-optimal equilibrium price vector in job-matching markets," Journal of Economic Theory, Elsevier, vol. 197(C).
    12. Yeon-Koo Che & Jinwoo Kim & Fuhito Kojima, 2019. "Weak Monotone Comparative Statics," Papers 1911.06442, arXiv.org, revised Nov 2021.
    13. Kyle Greenberg & Parag A. Pathak & Tayfun Sönmez, 2024. "Redesigning the US Army's Branching Process: A Case Study in Minimalist Market Design," American Economic Review, American Economic Association, vol. 114(4), pages 1070-1106, April.
    14. Naoyuki Kamiyama, 2022. "Strongly Stable Matchings under Matroid Constraints," Papers 2208.11272, arXiv.org, revised Sep 2022.
    15. Koji Yokote, 2020. "On optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraints," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 5(1), pages 37-77, December.
    16. Isa E. Hafalir & Fuhito Kojima & M. Bumin Yenmez & Koji Yokote, 2022. "Design on Matroids: Diversity vs. Meritocracy," Papers 2301.00237, arXiv.org.
    17. 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).
    18. Aygün, Orhan & Turhan, Bertan, 2019. "Matching with Generalized Lexicographic Choice Rules," ISU General Staff Papers 20191101070000, Iowa State University, Department of Economics.
    19. Thành Nguyen & Rakesh Vohra, 2019. "Stable Matching with Proportionality Constraints," Operations Research, INFORMS, vol. 67(6), pages 1503-1519, November.
    20. Yamaguchi, Tomoaki & Yahiro, Kentaro & Yokoo, Makoto, 2019. "Student-Project-Resource Matching-Allocation Problems: Game Theoretic Analysis," MPRA Paper 92720, University Library of Munich, Germany.
    21. Tayfun Sönmez & M. Bumin Yenmez, 2019. "Constitutional Implementation of Vertical and Horizontal Reservations in India: A Unified Mechanism for Civil Service Allocation and College Admissions," Boston College Working Papers in Economics 978, Boston College Department of Economics.
    22. Orhan Aygun & Bertan Turhan, 2020. "Designing Direct Matching Mechanism for India with Comprehensive Affirmative Action," Papers 2004.13264, arXiv.org, revised Dec 2021.
    23. Cho, Sung-Ho & Koshimura, Miyuki & Mandal, Pinaki & Yahiro, Kentaro & Yokoo, Makoto, 2022. "Impossibility of weakly stable and strategy-proof mechanism," Economics Letters, Elsevier, vol. 217(C).
    24. Haris Aziz & Florian Brandl, 2020. "The Vigilant Eating Rule: A General Approach for Probabilistic Economic Design with Constraints," Papers 2008.08991, arXiv.org, revised Jul 2021.
    25. Keisuke Bando & Kenzo Imamura & Yasushi Kawase, 2025. "Properties of Path-Independent Choice Correspondences and Their Applications to Efficient and Stable Matchings," Papers 2502.09265, arXiv.org.

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    More about this item

    Keywords

    Two-sided matching; Market design; Matching with contracts; Matching with constraints; Discrete convex analysis; Deferred acceptance;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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