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


  • HIRATA, Daisuke
  • KASUYA, Yusuke


This paper studies stable and (one-sided) strategy-proof matching rules in many-to-one matching markets with contracts. First, the number of such rules is shown to be at most one. Second, the doctor-optimal stable rule, whenever it exists, is shown to be the unique candidate for a stable and strategy-proof rule. Third, a stable and strategy-proof rule, when exists, is shown to be second-best optimal for doctor welfare, in the sense that no individually-rational and strategy-proof rule can dominate it. This last result is further generalized to non-wasteful and strategy-proof rules. Notably, all those results are established without any substitutes conditions on hospitals' choice functions, and hence, the proofs do not rely on the "rural hospital" theorem. We also show by example that the outcomes of a stable and strategy-proof rule do not always coincide with those of the cumulative offer process; hence, the above results hold NOT because the cumulative offer process is the only candidate for stable and strategy-proof rules.

Suggested Citation

  • HIRATA, Daisuke & KASUYA, Yusuke, 2015. "On Stable and Strategy-Proof Rules in Matching Markets with Contracts," Discussion Papers 2015-10, Graduate School of Economics, Hitotsubashi University.
  • Handle: RePEc:hit:econdp:2015-10

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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Nickesha Ayoade & Szilvia Pápai, 2020. "School Choice with Preference Rank Classes," Working Papers 20002, Concordia University, Department of Economics.
    3. Schlegel, Jan Christoph, 2020. "Equivalent choice functions and stable mechanisms," Games and Economic Behavior, Elsevier, vol. 123(C), pages 41-53.
    4. Michelle Avataneo & Bertan Turhan, 2020. "Slot-specific Priorities with Capacity Transfers," Papers 2004.13265,, revised Sep 2020.
    5. Afacan, Mustafa Oǧuz, 2020. "Graduate admission with financial support," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 114-127.
    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. HIRATA, Daisuke & KASUYA, Yusuke, 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.
    8. 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.

    More about this item


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

    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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