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Substitutes and stability for many-to-many matching with contracts

Author

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  • Bando, Keisuke
  • Hirai, Toshiyuki
  • Zhang, Jun

Abstract

We examine the roles of (slightly weakened versions of) the observable substitutability condition and the observable substitutability across doctors condition of Hatfield et al. (2021) in many-to-many matching with contracts. We modify the standard cumulative offer algorithm to find stable outcomes and prove new results on the existence of stable outcomes. It is remarkable that size monotonicity at the offer-proposing side is essential for the existence result under observable substitutability across doctors.

Suggested Citation

  • Bando, Keisuke & Hirai, Toshiyuki & Zhang, Jun, 2021. "Substitutes and stability for many-to-many matching with contracts," Games and Economic Behavior, Elsevier, vol. 129(C), pages 503-512.
    • Handle: RePEc:eee:gamebe:v:129:y:2021:i:c:p:503-512
    DOI: 10.1016/j.geb.2021.07.002
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    References listed on IDEAS

    as
    1. 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.
    2. Kominers, Scott Duke, 2012. "On the correspondence of contracts to salaries in (many-to-many) matching," Games and Economic Behavior, Elsevier, vol. 75(2), pages 984-989.
    3. Aygün, Orhan & Turhan, Bertan, 2020. "Dynamic reserves in matching markets," Journal of Economic Theory, Elsevier, vol. 188(C).
    4. Hatfield, John William & Kominers, Scott Duke, 2017. "Contract design and stability in many-to-many matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 78-97.
    5. Flanagan, Francis X., 2014. "Relaxing the substitutes condition in matching markets with contracts," Economics Letters, Elsevier, vol. 123(2), pages 113-117.
    6. Kadam, Sangram Vilasrao, 2017. "Unilateral substitutability implies substitutable completability in many-to-one matching with contracts," Games and Economic Behavior, Elsevier, vol. 102(C), pages 56-68.
    7. Tayfun Sönmez & Tobias B. Switzer, 2013. "Matching With (Branch‐of‐Choice) Contracts at the United States Military Academy," Econometrica, Econometric Society, vol. 81(2), pages 451-488, March.
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    More about this item

    Keywords

    Many-to-many matching; Stability; Observable substitutability; Size monotonicity; Cumulative offer algorithm;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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