Age-Based Preferences in Paired Kidney Exchange

We consider a model of Paired Kidney Exchange (PKE) with feasibility constraints on the number of patient-donor pairs involved in exchanges. Patients' preferences are restricted so that patients prefer kidneys from compatible younger donors to kidneys from older donors. In this framework, patients with compatible donors may enroll on PKE programs to receive an organ with higher expected graft survival than that of their intended donor. PKE rules that satisfy individual rationality, eciency, and strategy-proofness necessarily select pairwise exchanges. Such rules maximize the number of transplantations among pairs with the youngest donors, and sequentially among pairs with donors of dierent age group

New Challenges in Multihospital Kidney Exchange

The growth of kidney exchange presents new challenges for the design of kidney exchange clearinghouses. The players now include directors of transplant centers, who see sets of patient-donor pairs, and can choose to reveal only difficult-to-match pairs to the clearinghouse, while withholding easy-to-match pairs to transplant locally. This reduces the number of transplants. We discuss how the incentives for hospitals to enroll all pairs in kidney exchange can be achieved, and how the concentration of hard to match pairs increases the importance of long, non-simultaneous nondirected donor chains

Paired and altruistic kidney donation in the UK: Algorithms and experimentation

We study the computational problem of identifying optimal sets of kidney exchanges in the UK. We show how to expand an integer programming-based formulation due to Roth et al. [2007] in order to model the criteria that constitute the UK definition of optimality. The software arising from this work has been used by the National Health Service Blood and Transplant to find optimal sets of kidney exchanges for their National Living Donor Kidney Sharing Schemes since July 2008. We report on the characteristics of the solutions that have been obtained in matching runs of the scheme since this time. We then present empirical results arising from experiments on the real datasets that stem from these matching runs, with the aim of establishing the extent to which the particular optimality criteria that are present in the UK influence the structure of the solutions that are ultimately computed. A key observation is that allowing four-way exchanges would be likely to lead to a moderate number of additional transplants

Mix and match: a strategyproof mechanism for multi-hospital kidney exchange

As kidney exchange programs are growing, manipulation by hospitals becomes more of an issue. Assuming that hospitals wish to maximize the number of their own patients who receive a kidney, they may have an incentive to withhold some of their incompatible donor–patient pairs and match them internally, thus harming social welfare. We study mechanisms for two-way exchanges that are strategyproof, i.e., make it a dominant strategy for hospitals to report all their incompatible pairs. We establish lower bounds on the welfare loss of strategyproof mechanisms, both deterministic and randomized, and propose a randomized mechanism that guarantees at least half of the maximum social welfare in the worst case. Simulations using realistic distributions for blood types and other parameters suggest that in practice our mechanism performs much closer to optimal

Paired and altruistic kidney donation in the UK: algorithms and experimentation

We study the computational problem of identifying optimal sets of kidney exchanges in the UK. We show how to expand an integer programming-based formulation [1, 19] in order to model the criteria that constitute the UK definition of optimality. The software arising from this work has been used by the National Health Service Blood and Transplant to find optimal sets of kidney exchanges for their National Living Donor Kidney Sharing Schemes since July 2008.We report on the characteristics of the solutions that have been obtained in matching runs of the scheme since this time. We then present empirical results arising from the real datasets that stem from these matching runs, with the aim of establishing the extent to which the particular optimality criteria that are present in the UK influence the structure of the solutions that are ultimately computed. A key observation is that allowing 4-way exchanges would be likely to lead to a significant number of additional transplants

Operation Frames and Clubs in 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. We prove that unlike in the standard model, the uncapped clearing problem is NP-complete. We also 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. Experiments show that in the single-donation setting, operation frames improve planning by 34%--51%. Allowing up to two donors to donate in exchange for one kidney donated to their designated patient yields a further increase in social welfare.Comment: Published at IJCAI-1

Mix and match: A strategyproof mechanism for multi-hospital kidney exchange

As kidney exchange programs are growing, manipulation by hospitals becomes more of an issue. Assuming that hospitals wish to maximize the number of their own patients who receive a kidney, they may have an incentive to withhold some of their incompatible donor-patient pairs and match them internally, thus harming social welfare. We study mechanisms for two-way exchanges that are strategyproof, i.e., make it a dominant strategy for hospitals to report all their incompatible pairs. We establish lower bounds on the welfare loss of strategyproof mechanisms, both deterministic and randomized, and propose a randomized mechanism that guarantees at least half of the maximum social welfare in the worst case. Simulations using realistic distributions for blood types and other parameters suggest that in practice our mechanism performs much closer to optimal. Keywords: Approximate mechanisms without money; Kidney exchang