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Restricted complementarity and paths to stability in matching with couples

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  • Tello, Benjamín

Abstract

We study matching with couples problems where hospitals have one vacant position. We introduce a constraint on couples’ preferences over pairs of hospitals called restricted complementarity, which is a “translation” of bilateral substitutability in matching with contracts. Next, we extend Klaus and Klijn’s (2007) path to stability result by showing that if couples’ preferences satisfy restricted complementarity, then from any arbitrary matching, there exists a finite path of matchings where each matching on the path is obtained by “satisfying” a blocking coalition for the previous one and the final matching is stable.

Suggested Citation

  • Tello, Benjamín, 2023. "Restricted complementarity and paths to stability in matching with couples," Mathematical Social Sciences, Elsevier, vol. 126(C), pages 60-67.
    • Handle: RePEc:eee:matsoc:v:126:y:2023:i:c:p:60-67
    DOI: 10.1016/j.mathsocsci.2023.09.005
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    References listed on IDEAS

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    1. Ata Atay & Sylvain Funck & Ana Mauleon & Vincent Vannetelbosch, 2023. "Matching markets with farsighted couples," UB School of Economics Working Papers 2023/445, University of Barcelona School of Economics.
    2. Klaus, Bettina & Klijn, Flip, 2007. "Paths to stability for matching markets with couples," Games and Economic Behavior, Elsevier, vol. 58(1), pages 154-171, January.
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    7. 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.
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    9. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July.
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