Kidney exchange programs (KEPs) form an innovative approach to increasing the donor pool through allowing the participation of renal patients together with a willing but incompatible donor. The aim of a KEP is to identify groups of incompatible donor-recipient pairs that could exchange donors leading to feasible transplants. As the size of a kidney exchange grows, a larger proportion of participants can be transplanted. Collaboration between multiple transplant centers, by merging their separate kidney exchange pools is thus desirable. As each transplant center has its own interest to provide the best care to its own patients, collaboration requires balancing individual and common objectives. We consider a class of algorithmic mechanisms for multi-center kidney exchange programs we call rejection-proof mechanisms. Such mechanisms propose solutions with the property that no player wishes to unilaterally deviate. We provide a mechanism optimizing social value under this restriction, though the underlying optimization problem is Sigma-2-p-Hard. We also describe a computationally easier but sub-optimal alternative. Experiments show that rejection-proofness can be achieved at limited cost compared to optimal solutions for regular kidney exchange. Computationally, we provide algorithms to compute optimal rejection-proof solutions for small and medium instance sizes.
