Inter-Club Kidney Exchange

A kidney exchange is a centrally-administered barter market where patients swap their willing yet incompatible donors. Modern kidney exchanges use 2-cycles, 3-cycles, and chains initiated by non-directed donors (altruists who are willing to give a kidney to anyone) as the means for swapping. We propose significant generalizations to kidney exchange. We allow more than one donor to donate in exchange for their desired patient receiving a kidney. We also allow for the possibility of a donor willing to donate if any of a number of patients receive kidneys. Furthermore, we combine these notions and generalize them.The generalization is to exchange among organ clubs, where a club is willing to donate organs outside the club if and only if the club receives organs from outside the club according to given specifications. Forms of organ clubs already exist — under an arrangement where one gets to be in the club as a potential recipient if one is willing to donate one's organs to the club upon death. Our approach can be used as an inter-club exchange mechanism that increases systemwide good (and can also be applied to live donation). In this paper we introduce these ideas, present the notion of operation frames that can be used to sequence the operations across batches, and present integer programming formulations for the market clearing problems for these new types of organ exchanges.