Stable Allocations with Network-Based Comparisons

Hatfield and Milgrom (2005) present a unified model of matching with contracts phrased in terms of hospitals and doctors, which subsumes the standard two-sided matching and some package auction models. They show that a stable allocation exists if contracts are substitutes for each hospital. They further claim that if a hospital's preferences violate the substitutes condition, there exist singleton preferences for the other hospitals and doctors such that no stable allocation exists. We show this last claim does not hold in general. We further present a weaker condition that is necessary to guarantee the existence of stable allocations. (JEL C78, D86, J41)

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Stable Allocations of Risk

SSRN Electronic Journal ◽

10.2139/ssrn.1853577 ◽

2007 ◽

Author(s):

P. Jean-Jacques Herings ◽

Péter Csóka ◽

Laszlo A. Koczy

Keyword(s):

Stable Allocations

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Matching in Networks with Bilateral Contracts

American Economic Journal Microeconomics ◽

10.1257/mic.4.1.176 ◽

2012 ◽

Vol 4 (1) ◽

pp. 176-208 ◽

Cited By ~ 50

Author(s):

John William Hatfield ◽

Scott Duke Kominers

Keyword(s):

Supply Chain ◽

Lattice Structure ◽

Chain Structure ◽

Rural Hospitals ◽

Classical Lattice ◽

Maximal Domain ◽

Bilateral Contracts ◽

Supply Chain Structure ◽

Stable Allocations ◽

Strategy Proofness

We introduce a model in which firms trade goods via bilateral contracts which specify a buyer, a seller, and the terms of the exchange. This setting subsumes (many-to-many) matching with contracts, as well as supply chain matching. When firms' relationships do not exhibit a supply chain structure, stable allocations need not exist. By contrast, in the presence of supply chain structure, a natural substitutability condition characterizes the maximal domain of firm preferences for which stable allocations are guaranteed to exist. Furthermore, the classical lattice structure, rural hospitals theorem, and one-sided strategy-proofness results all generalize to this setting. (JEL C78, D85, D86, L14)

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