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Unilateral substitutability implies substitutable completability in many-to-one matching with contracts

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  • Kadam, Sangram Vilasrao

Abstract

We prove that the unilateral substitutability property introduced in Hatfield and Kojima (2010) implies the substitutable completability property from Hatfield and Kominers (2014). This paper provides a novel linkage between these two sufficient conditions for the existence of a stable matching in many-to-one matching markets with contracts. A substitutable completion of a preference is a substitutable preference created by adding some sets of contracts to the original preference order. We provide an algorithm which when operated on the unilaterally substitutable preferences produces such a substitutable completion. Thus it provides a constructive proof of the connection between the two properties.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:gamebe:v:102:y:2017:i:c:p:56-68
    DOI: 10.1016/j.geb.2016.10.002
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    2. Hirata, Daisuke & 平田, 大祐 & Kasuya, Yusuke & 糟谷, 祐介 & Okumura, Yasunori & 奥村, 保規, 2023. "Stability, Strategy-Proofness, and Respect for Improvements," Discussion Papers 2023-01, Graduate School of Economics, Hitotsubashi University.
    3. Ravi Jagadeesan, 2019. "Cadet-Branch Matching in a Kelso-Crawford Economy," American Economic Journal: Microeconomics, American Economic Association, vol. 11(3), pages 191-224, August.
    4. 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.
    5. Hassidim, Avinatan & Romm, Assaf & Shorrer, Ran I., 2019. "Contracts are not salaries in the hidden-substitutes domain," Economics Letters, Elsevier, vol. 181(C), pages 40-42.

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    More about this item

    Keywords

    Many-to-one matching; Matching with contracts; Unilateral substitutability; Substitutable completability;
    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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