  A kidney exchange program, also called a kidney paired donation program, can
be viewed as a repeated, dynamic trading and allocation mechanism. This
suggests that a dynamic algorithm for transplant exchange selection may have
superior performance in comparison to the repeated use of a static algorithm.
We confirm this hypothesis using a full scale simulation of the Canadian Kidney
Paired Donation Program: learning algorithms, that attempt to learn optimal
patient-donor weights in advance via dynamic simulations, do lead to improved
outcomes. Specifically, our learning algorithms, designed with the objective of
fairness (that is, equity in terms of transplant accessibility across cPRA
groups), also lead to an increased number of transplants and shorter average
waiting times. Indeed, our highest performing learning algorithm improves
egalitarian fairness by 10% whilst also increasing the number of transplants by
6% and decreasing waiting times by 24%. However, our main result is much more
surprising. We find that the most critical factor in determining the
performance of a kidney exchange program is not the judicious assignment of
positive weights (rewards) to patient-donor pairs. Rather, the key factor in
increasing the number of transplants, decreasing waiting times and improving
group fairness is the judicious assignment of a negative weight (penalty) to
the small number of non-directed donors in the kidney exchange program.
