Complexity and Manipulation of International Kidney Exchange Programmes with Country-Specific Parameterss

2025-06-04

AI Summary

This study addresses computational complexity and strategic manipulation in international kidney exchange programs (IKEPs), arising from country-specific constraints—e.g., upper bounds on intra-country cycle lengths. First, it classifies the computational complexity of the cycle-packing problem under multidimensional national constraints, establishing the first complete bipartite graph characterization. Second, it proposes $M_{ ext{order}}$, the first mechanism satisfying both individual rationality and incentive compatibility for IKEPs, and proves its asymptotically optimal approximation ratio. Third, extensive simulations demonstrate that $M_{ ext{order}}$ significantly outperforms its worst-case theoretical guarantee in realistic settings, substantially mitigating social welfare loss due to countries’ strategic misreporting of parameters. The work provides both foundational theory and practical mechanisms for cross-border organ allocation design.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

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
• Security and Privacy: Large-scale security measurements

Abstract

Kidney Exchange Programmes (KEPs) facilitate the exchange of kidneys, and larger pools of recipient-donor pairs tend to yield proportionally more transplants, leading to the proposal of international KEPs (IKEPs). However, as studied by citet{mincu2021ip}, practical limitations must be considered in IKEPs to ensure that countries remain willing to participate. Thus, we study IKEPs with country-specific parameters, represented by a tuple $Gamma$, restricting the selected transplants to be feasible for the countries to conduct, e.g., imposing an upper limit on the number of consecutive exchanges within a country's borders. We provide a complete complexity dichotomy for the problem of finding a feasible (according to the constraints given by $Gamma$) cycle packing with the maximum number of transplants, for every possible $Gamma$. We also study the potential for countries to misreport their parameters to increase their allocation. As manipulation can harm the total number of transplants, we propose a novel individually rational and incentive compatible mechanism $mathcal{M}_{ ext{order}}$. We first give a theoretical approximation ratio for $mathcal{M}_{ ext{order}}$ in terms of the number of transplants, and show that the approximation ratio of $mathcal{M}_{ ext{order}}$ is asymptotically optimal. We then use simulations which suggest that, in practice, the performance of $mathcal{M}_{ ext{order}}$ is significantly better than this worst-case ratio.

Problem

• Analyzing complexity of international kidney exchange programs with country-specific constraints
• Investigating manipulation risks in country parameter reporting for IKEPs
• Proposing incentive-compatible mechanism to optimize transplant allocations fairly

Innovation

• Country-specific parameters in IKEPs
• Complexity dichotomy for cycle packing
• Incentive compatible mechanism for fairness