Computing Balanced Solutions for Large International Kidney Exchange Schemes

TL;DR

This paper introduces a computational approach to optimize fairness in large international kidney exchange schemes by balancing country allocations using advanced matching algorithms, demonstrating significant improvements in fairness and scalability.

Contribution

It presents the first large-scale computational study of balancing solutions in IKEPs, comparing multiple allocation concepts and demonstrating the effectiveness of lexicographically minimal matchings.

Findings

Lexicographically minimal matchings improve fairness by up to 54%.

State-of-the-art software enables computation for up to 15 countries.

Hard-to-compute concepts like Shapley value are now feasible for larger schemes.

Abstract

To overcome incompatibility issues, kidney patients may swap their donors. In international kidney exchange programmes (IKEPs), countries merge their national patient-donor pools. We consider a recently introduced credit system. In each round, countries are given an initial ``fair'' allocation of the total number of kidney transplants. This allocation is adjusted by a credit function yielding a target allocation. The goal is to find a solution that approaches the target allocation as closely as possible, to ensure long-term stability of the international pool. As solutions, we use maximum matchings that lexicographically minimize the country deviations from the target allocation. We perform, for the first time, a computational study for a {\it large} number of countries. For the initial allocations we use two easy-to-compute solution concepts, the benefit value and the contribution value, and four classical but hard-to-compute concepts, the Shapley value, nucleolus, Banzhaf value and tau value. By using state-of-the-art software we show that the latter four concepts are now within reach for IKEPs of up to fifteen countries. Our experiments show that using lexicographically minimal maximum matchings instead of ones that only minimize the largest deviation from the target allocation (as previously done) may make an IKEP up to 54% more balanced.