Abstract
This paper studies a general kidney exchange model with compatible patient-donor pairs, incompatible patient-donor pairs, single donors, and patients on the waiting list. We derive an explicit formula of the maximal number of feasible kidney transplants under several sizes of cycles and chains of exchange, analyze the effect of different ways of exchange on efficiency, and provide substantial simulation results based on the USA data. Our results further show that kidney exchange can be decentralized for relatively large populations, and that allowing compatible pairs and single donors to exchange with incompatible pairs can significantly increase the number of feasible kidney transplants. A more general model of two-category type-compatible exchanges is also established.
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