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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

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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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