Substitutes and stability for matching with contracts

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 s...

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Bibliographic Details
Published in:Journal of economic theory 2010-09, Vol.145 (5), p.1704-1723
Main Authors: Hatfield, John William, Kojima, Fuhito
Format: Article
Language:English
Subjects:
Allocations
Bilateral substitutes
Contracts
Doctors
Economic models
Economic theory
Economics
Group strategy-proofness
Health economics
Hospital management
Hospitals
Incentives
Lattice
Lattices
Law of aggregate demand
Matching
Matching with contracts
Mathematical economics
Preferences
Resource allocation
Rural hospitals theorem
Stability
Strategy-proofness
Studies
Substitutes
Substitutes Bilateral substitutes Unilateral substitutes Matching Matching with contracts Law of aggregate demand Stability Strategy-proofness Rural hospitals theorem Group strategy-proofness Lattice
Unilateral substitutes
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Summary: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.
ISSN:0022-0531
1095-7235
DOI:10.1016/j.jet.2010.01.007