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Substitutes and stability for matching with contracts

  • Hatfield, John William
  • Kojima, Fuhito
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    We consider the matching with contracts framework of Hatfield and Milgrom [20], and we introduce new concepts of bilateral and unilateral substitutes. We show that the bilateral substitutes condition is a sufficient condition for the existence of a stable allocation in this framework. However, the set of stable allocations does not form a lattice under this condition, and there does not necessarily exist a doctor-optimal stable allocation. Under a slightly stronger condition, unilateral substitutes, the set of stable allocations still does not necessarily form a lattice with respect to doctors' preferences, but there does exist a doctor-optimal stable allocation, and other key results such as incentive compatibility and the rural hospitals theorem are recovered.

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    Article provided by Elsevier in its journal Journal of Economic Theory.

    Volume (Year): 145 (2010)
    Issue (Month): 5 (September)
    Pages: 1704-1723

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    Handle: RePEc:eee:jetheo:v:145:y:2010:i:5:p:1704-1723
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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    6. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May.
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    16. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2000. "Single Agents and the Set of Many-to-One Stable Matchings," Journal of Economic Theory, Elsevier, vol. 91(1), pages 91-105, March.
    17. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-27, June.
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    21. Alvin E. Roth & Uriel G. Rothblum, 1999. "Truncation Strategies in Matching Markets--In Search of Advice for Participants," Econometrica, Econometric Society, vol. 67(1), pages 21-44, January.
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