Core-Stable Kidney Exchange via Altruistic Donors

TL;DR

This paper introduces a method to ensure stability in kidney exchange programs by adding altruistic donors, demonstrating that only a small number of altruists are needed in realistic scenarios to maintain core stability.

Contribution

The paper proposes a novel approach using altruistic donors to restore core stability in kidney exchanges, with theoretical bounds and practical simulations showing efficiency.

Findings

Few altruists are needed in realistic settings.

Altruist requirement grows logarithmically with market size in random graphs.

Proportional altruist allocation suffices when small cycles are allowed.

Abstract

Kidney exchange programs among hospitals in the United States and across European countries improve efficiency by pooling donors and patients on a centralized platform. Sustaining such cooperation requires stability. When the core is empty, hospitals or countries may withhold easily matched pairs for internal use, creating incentive problems that undermine participation and reduce the scope and efficiency of exchange. We propose a method to restore core stability by augmenting the platform with altruistic donors. Although the worst-case number of required altruists can be large, we show that in realistic settings only a small number is needed. We analyze two models of the compatibility graph, one based on random graphs and the other on compatibility types. When only pairwise exchanges are allowed, the number of required altruists is bounded by the maximum number of independent odd cycles, defined as disjoint odd cycles with no edges between them. This bound grows logarithmically with market size in the random graph model and is at most one third of the number of compatibility types in the type-based model. When small exchange cycles are allowed, it suffices for each participating organization to receive a number of altruists proportional to the number of compatibility types. Finally, simulations show that far fewer altruists are needed in practice than worst-case theory suggests.