Core-Stable Kidney Exchange via Altruistic Donors

2026-02-11

AI Summary

This study addresses the core instability in kidney exchange platforms, which often arises when participating institutions withhold easily matched donor–recipient pairs to gain strategic advantage, thereby undermining overall efficiency. The work proposes the systematic incorporation of altruistic donors as a novel mechanism to restore core stability and demonstrates that only a small number are required to eliminate incentives for participants to withdraw. By integrating random graph models with compatibility-type analysis, the authors characterize odd-cycle structures and leverage tools from graph theory and mechanism design to derive an upper bound on the requisite number of altruistic donors—showing it grows logarithmically with market size or linearly with the number of compatibility types. Simulations confirm that actual requirements are substantially lower than worst-case theoretical bounds, underscoring the approach’s practicality and efficiency.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• kidney exchange
• core stability
• altruistic donors
• incentive compatibility
• cooperative matching

Innovation

• core stability
• altruistic donors
• kidney exchange
• compatibility graph
• odd cycles