American Economic Review · 2008 · 121 citations · 23 references
BusinessEconomicsContract TheoryContractsStandard Form ContractsContract DesignMatching TheoryOptimal ContractingExistence Of Stable MatchingsMatching Equilibrium ExistenceMatching With Contracts
Hatfield and Milgrom (2005) introduced a unified matching‑with‑contracts framework for hospitals and doctors, proving that a stable allocation exists when hospital contracts are substitutes and claiming that violating this condition can preclude stability. We demonstrate that the claimed necessity of the substitutes condition for stability is false in general and propose a weaker requirement that still ensures stable allocations. JEL codes: C78, D86, J41.
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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