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Substitutes and Stability in Matching with Contracts

Author(s): 
John William Hatfield and Fuhito Kojima
日付: 
Wed, 2008-09-17
Abstract: 
We consider the matching with contracts framework of Hatfield and Milgrom (2005), and we introduce new concepts of bilateral and unilateral substitutes. We show that bilateral substitutes 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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