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Unilateral Substitutability implies Substitutable completability in many-to-one matching with contracts

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  • Kadam, Sangram V

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.

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  • Kadam, Sangram V, 2014. "Unilateral Substitutability implies Substitutable completability in many-to-one matching with contracts," Working Paper 139666, Harvard University OpenScholar.
    • Handle: RePEc:qsh:wpaper:139666
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    Cited by:

    1. 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.
    2. 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.
    3. Jan Christoph Schlegel, 2014. "Contracts versus Salaries in Matching: A General Result. N.B.: This paper replaces Nr 13.09 "Contracts versus Salaries in Matching: Comment", (June 2013)," Cahiers de Recherches Economiques du Département d'économie 14.05, Université de Lausanne, Faculté des HEC, Département d’économie.
    4. Zhang, Jun, 2016. "On sufficient conditions for the existence of stable matchings with contracts," Economics Letters, Elsevier, vol. 145(C), pages 230-234.

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