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Near Feasible Stable Matchings with Complementarities

Author

Listed:
  • Thanh Nguyen

    (Krannert School of Management, Purdue University)

  • Rakesh Vohra

    (Department of Economics, University of Pennsylvania)

Abstract
The National Resident Matching program strives for a stable matching of medical students to teaching hospitals. With the presence of couples, stable matchings need not exist. For any student preferences, we show that each instance of a stable matching problem has a ’nearby’ instance with a table matching. The nearby instance is obtained by perturbing the capacities of the hospitals. Specifically, given a reported capacity for each hospital h, we find a redistribution of the slot capacities k¹h satisfying [kh –k¹h] ≤ 4 for all hospital h, and ∑h kh ≤ ∑ k¹h ≤ ∑h kh + 9, such that a stable matching exists with respect to k¹. Our approach is general and applies to other type of complementarities, as well as matchings with side constraints and contracts.

Suggested Citation

  • Thanh Nguyen & Rakesh Vohra, 2014. "Near Feasible Stable Matchings with Complementarities," PIER Working Paper Archive 14-028, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    • Handle: RePEc:pen:papers:14-028
    as

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    File URL: https://economics.sas.upenn.edu/sites/default/files/filevault/14-028_0.pdf
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    References listed on IDEAS

    as
    1. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
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    7. repec:ebl:ecbull:v:3:y:2004:i:45:p:1-11 is not listed on IDEAS
    8. 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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    16. Peter Biro & Tamas Fleiner, 2012. "Fractional solutions for capacitated NTU-games, with applications to stable matchings," CERS-IE WORKING PAPERS 1234, Institute of Economics, Centre for Economic and Regional Studies.
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    Cited by:

    1. Elizabeth Baldwin & Paul Klemperer, 2019. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities," Econometrica, Econometric Society, vol. 87(3), pages 867-932, May.
    2. Tello, Benjamín, 2016. "Matching with contracts, substitutes and two-unit demand," Economics Letters, Elsevier, vol. 146(C), pages 85-88.

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    More about this item

    Keywords

    stable matching; complementarities; Scarf's lemma;
    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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