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Unilateral substitutability is necessary for doctor-optimal stability

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  • Kasuya, Yusuke

Abstract

In the standard matching with contracts setting, the unilateral substitutability condition (Hatfield and Kojima, 2010) is known to be sufficient for the guaranteed existence of a doctor-optimal stable allocation. We show that the same condition is indeed necessary under observable substitutability across doctors (Hatfield, Kominers and Westkamp, 2020) while also necessary in the maximal domain sense in general for its guaranteed existence.

Suggested Citation

  • Kasuya, Yusuke, 2021. "Unilateral substitutability is necessary for doctor-optimal stability," Economics Letters, Elsevier, vol. 207(C).
    • Handle: RePEc:eee:ecolet:v:207:y:2021:i:c:s0165176521003244
    DOI: 10.1016/j.econlet.2021.110047
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    References listed on IDEAS

    as
    1. Kominers, Scott Duke & Sönmez, Tayfun, 2016. "Matching with slot-specific priorities: theory," Theoretical Economics, Econometric Society, vol. 11(2), May.
    2. Orhan Ayg?n & Tayfun S?nmez, 2013. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 103(5), pages 2050-2051, August.
    3. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    4. Kyle Greenberg & Parag A. Pathak & Tayfun Sönmez, 2021. "Redesigning the US Army’s Branching Process: A Case Study in Minimalist Market Design," NBER Working Papers 28911, National Bureau of Economic Research, Inc.
    5. Hatfield, John William & Kojima, Fuhito, 2010. "Substitutes and stability for matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1704-1723, September.
    6. Hirata, Daisuke & Kasuya, Yusuke, 2017. "On stable and strategy-proof rules in matching markets with contracts," Journal of Economic Theory, Elsevier, vol. 168(C), pages 27-43.
    7. Hirata, Daisuke & Kasuya, Yusuke, 2014. "Cumulative offer process is order-independent," Economics Letters, Elsevier, vol. 124(1), pages 37-40.
    8. Hatfield, John William & Kojima, Fuhito, 2009. "Group incentive compatibility for matching with contracts," Games and Economic Behavior, Elsevier, vol. 67(2), pages 745-749, November.
    9. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
    10. Crawford, Vincent P., 1991. "Comparative statics in matching markets," Journal of Economic Theory, Elsevier, vol. 54(2), pages 389-400, August.
    11. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Matching with contracts; Doctor-optimal stability; Unilateral substitutability; Observable substitutability across doctors;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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