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.

翻译：美国及欧洲各国医院间的肾脏交换计划通过将捐赠者与患者汇集于集中平台来提高匹配效率。维持此类合作需要稳定性保障。当核心为空时，医院或国家可能扣留易匹配的配对供内部使用，由此产生的激励问题会削弱参与意愿，缩减交换规模与效率。本文提出通过引入利他主义捐赠者来增强平台功能，从而恢复核心稳定性的方法。尽管所需利他主义捐赠者在最坏情况下可能数量庞大，但我们证明在实际场景中仅需少量捐赠者即可实现目标。我们分析了两种相容性图模型：一种基于随机图，另一种基于相容性类型。当仅允许两两交换时，所需利他主义捐赠者数量受限于最大独立奇环数（即彼此间无边相连的互斥奇环）。该上界在随机图模型中随市场规模呈对数增长，在基于类型的模型中不超过相容性类型总数的三分之一。当允许小型交换环时，每个参与机构获得的利他主义捐赠者数量仅需与相容性类型数量成比例。最终仿真结果表明，实际所需利他主义捐赠者数量远少于最坏情况理论值。