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On Stable and Strategy-Proof Rules in Matching Markets with Contracts

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  • HIRATA, Daisuke
  • 平田, 大祐
  • KASUYA, Yusuke
  • 糟谷, 祐介

Abstract

This paper studies stable and (one-sided) strategy-proof rules in many-to-one matching markets with contracts. Not assuming any kind of substitutes condition or the law of aggregate demand, we obtain the following results. First, the number of stable and strategy-proof rules is at most one. Second, the doctor-optimal stable rule, whenever it exists, is the unique candidate for a stable and strategy-proof rule. Third, a stable and strategy-proof rule, whenever it exists, is second-best optimal for doctor welfare, in that no individually rational and strategy-proof rule can dominate it. This last result is further generalized to non-wasteful and strategy-proof rules. Due to the weak assumptions, our analysis covers a broad range of markets, including cases where a (unique) stable and strategy-proof rule is not equal to the one induced by the cumulative offer process or the deferred acceptance algorithm.
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Suggested Citation

  • HIRATA, Daisuke & 平田, 大祐 & KASUYA, Yusuke & 糟谷, 祐介, 2016. "On Stable and Strategy-Proof Rules in Matching Markets with Contracts," Discussion Papers 2016-13, Graduate School of Economics, Hitotsubashi University.
    • Handle: RePEc:hit:econdp:2016-13
    Note: This Version: December, 2016
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    File URL: https://hermes-ir.lib.hit-u.ac.jp/hermes/ir/re/28238/070econDP16-13.pdf
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. Sirguiado, Camilo J. & Torres-Martínez, Juan Pablo, 2024. "Strategic behavior in one-to-one matching markets without outside options," Games and Economic Behavior, Elsevier, vol. 148(C), pages 385-397.
    2. 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.
    3. Avataneo, Michelle & Turhan, Bertan, 2021. "Slot-specific priorities with capacity transfers," Games and Economic Behavior, Elsevier, vol. 129(C), pages 536-548.
    4. 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.
    5. Battal Dou{g}an & Kenzo Imamura & M. Bumin Yenmez, 2022. "Market Design with Deferred Acceptance: A Recipe for Policymaking," Papers 2209.06777, arXiv.org.
    6. Jan Christoph Schlegel, 2016. "Virtual Demand and Stable Mechanisms," Cahiers de Recherches Economiques du Département d'économie 16.11, Université de Lausanne, Faculté des HEC, Département d’économie.
    7. Kasuya, Yusuke, 2021. "Unilateral substitutability is necessary for doctor-optimal stability," Economics Letters, Elsevier, vol. 207(C).
    8. Adriana Amieva & Agust'in G. Bonifacio & Pablo Neme, 2024. "Mechanisms for a dynamic many-to-many school choice problem," Papers 2411.07851, arXiv.org, revised May 2025.
    9. Afacan, Mustafa Oǧuz, 2020. "Graduate admission with financial support," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 114-127.
    10. Kasuya, Yusuke, 2021. "Group incentive compatibility and welfare for matching with contracts," Economics Letters, Elsevier, vol. 202(C).
    11. Yusuke Iwase, 2022. "Equivalence theorem in matching with contracts," Review of Economic Design, Springer;Society for Economic Design, vol. 26(1), pages 117-125, March.
    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.
    13. Zhang, Jun, 2023. "Strategy-proof allocation with outside option," Games and Economic Behavior, Elsevier, vol. 137(C), pages 50-67.
    14. Schlegel, Jan Christoph, 2020. "Equivalent choice functions and stable mechanisms," Games and Economic Behavior, Elsevier, vol. 123(C), pages 41-53.
    15. Mustafa Oǧuz Afacan, 2016. "Characterizations of the cumulative offer process," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 531-542, October.
    16. Tayfun Sonmez & M. Bumin Yenmez, 2022. "Constitutional Implementation of Affirmative Action Policies in India," Papers 2203.01483, arXiv.org, revised Mar 2024.
    17. Tierney, Ryan, 2022. "Incentives And Efficiency In Matching With Transfers: Towards Nonquasilinear Package Auctions," Discussion Papers on Economics 6/2022, University of Southern Denmark, Department of Economics.
    18. Alva, Samson & Manjunath, Vikram, 2019. "Strategy-proof Pareto-improvement," Journal of Economic Theory, Elsevier, vol. 181(C), pages 121-142.
    19. Ayoade, Nickesha & Pápai, Szilvia, 2023. "School choice with preference rank classes," Games and Economic Behavior, Elsevier, vol. 137(C), pages 317-341.
    20. Kyle Greenberg & Parag A. Pathak & Tayfun Sönmez, 2020. "Mechanism Design meets Priority Design: Redesigning the US Army’s Branching Process Through Market Design," Boston College Working Papers in Economics 1035, Boston College Department of Economics.
    21. Iwase, Yusuke & Tsuruta, Shoya & Yoshimura, Akina, 2022. "Nash implementation on the basis of general priorities," Games and Economic Behavior, Elsevier, vol. 132(C), pages 368-379.
    22. Kyle Greenberg & Parag A. Pathak & Tayfun Sonmez, 2021. "Mechanism Design meets Priority Design: Redesigning the US Army's Branching Process," Papers 2106.06582, arXiv.org.
    23. HIRATA, Daisuke & 平田, 大祐 & KASUYA, Yusuke & 糟谷, 祐介, 2016. "Supplementary Note to “On Stable and Strategy-Proof Rules in Matching Markets with Contracts”," Discussion Papers 2016-14, Graduate School of Economics, Hitotsubashi University.
    24. Camilo J. Sirguiado & Juan Pablo Torres-Martinez, 2024. "Strategic Behavior Without Outside Options," Working Papers wp553, University of Chile, Department of Economics.

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    More about this item

    Keywords

    matching with contracts; stability; strategy-proofness; uniqueness; efficiency; irrelevance of rejected contracts;
    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

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