Kidney Exchange with Immunosuppressants∗

This paper investigates implications of introducing immunosuppressants (or suppressants) in kidney exchange problems. We begin with the standard kidney exchange model without suppressants and define two versions of the top-trading cycles (TTC) solutions satisfying Pareto efficiency. We then extend the model by introducing suppressants that make a patient compatible with any donor by relaxing immunological compatibility constraints. We examine the existence of solutions satisfying Pareto efficiency together with “monotonicity” and “maximal improvement”. Monotonicity requires that no patient should get worse off after the introduction of suppressants. Maximal improvement requires that if one set of recipients of suppressants enables more transplantations than the other (in terms of set inclusion), then the latter should not be chosen as the set of recipients. We propose two modified versions of TTC solutions satisfying these requirements. We also provide simulation analyses based on the actual transplantation data to see how much reduction we can expect on the current practice of using suppressants. In a blood-type restricted environment, we introduce an algorithm that minimizes the use of suppressants, given that all patients in the data receive transplantations. Our simulation result suggests that the use of suppressants can be reduced by 55 percent when the recipients of suppressants are chosen as we propose. JEL classification Numbers: C71; D02; D63; I10