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

TL;DR

This paper analyzes the complexity and strategic manipulation in international kidney exchange programs with country-specific constraints, proposing a mechanism that ensures fairness and efficiency in transplant allocations.

Contribution

It provides a complete complexity classification for feasible cycle packing under country-specific parameters and introduces a mechanism that is both incentive compatible and individually rational.

Findings

Complexity dichotomy for maximum feasible transplants under country constraints.

A novel mechanism $\\mathcal{M}_{\text{order}}$ that is incentive compatible and rational.

Simulations show practical performance exceeds theoretical guarantees.

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 $\mathcal{M}_{\text{order}}$. We first give a theoretical approximation ratio for $\mathcal{M}_{\text{order}}$ in terms of the number of transplants, and show that the approximation ratio of $\mathcal{M}_{\text{order}}$ is asymptotically optimal. We then use simulations which suggest that, in practice, the performance of $\mathcal{M}_{\text{order}}$ is significantly better than this worst-case ratio.