Partitioned Matching Games for International Kidney Exchange

Benedek, Márton; Bíró, Péter; Kern, Walter; Pálvölgyi, Dömötör; Paulusma, Daniël

doi:10.48550/arxiv.2301.13181

Cited by 1 publication

(6 citation statements)

References 32 publications

(57 reference statements)

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“…In [12], the polynomial-time algorithm of [19] was generalized to a polynomial-time algorithm for computing a maximum matching that lexicographically minimizes the country deviations from a given target allocation. In [10], the theoretical results from [12] and [19] are unified and extended.…”

Section: Our Settingmentioning

confidence: 99%

“…As we will explain, this algorithm can also be used for computing maximum matchings that minimize only the largest country deviation from a given target allocation. For the correctness proof and a running time analysis of the algorithm we refer to [12] (see also [10]).…”

Section: Our Contributionsmentioning

confidence: 99%

“…. , d t , the algorithm calls the polynomial-time algorithm provided by the following lemma from [12] (see also [10]).…”

Section: Computing a Lexicographically Minimal Maximum Matchingmentioning

confidence: 99%

“…Note that Lex-Min terminates as soon as all countries are finished. For a correctness proof and running time analysis of Lex-Min we refer to [12] (see also [10]).…”

Section: Lemma 1 ([12]mentioning

confidence: 99%

“…We therefore use the Lexicographical Descent method of [13], which is the state-of-the-art method in nucleolus computation. 10 Solutions. As mentioned, we aim to examine the benefits of using solutions maximum matchings prescribed by Lex-Min over arbitrary matchings or maximum matchings that minimize the maximum deviation d 1 from the target allocation.…”

Section: Simulations Detailsmentioning

confidence: 99%

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Computing Balanced Solutions for Large International Kidney Exchange Schemes

Benedek

Bíró

Kern

et al. 2023

Preprint

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To overcome incompatibility issues, kidney patients may swap their donors. In international kidney exchange programmes (IKEPs), countries merge their national patient-donor pools. We consider a recently introduced credit system. In each round, countries are given an initial ``fair'' allocation of the total number of kidney transplants. This allocation is adjusted by a credit function yielding a target allocation. The goal is to find a solution that approaches the target allocation as closely as possible, to ensure long-term stability of the international pool. As solutions, we use maximum matchings that lexicographically minimize the country deviations from the target allocation. We perform, for the first time, a computational study for a large number of countries. For the initial allocations we use two easy-to-compute solution concepts, the benefit value and the contribution value, and four classical but hard-to-compute concepts, the Shapley value, nucleolus, Banzhaf value and tau value. By using state-of-the-art software we show that the latter four concepts are now within reach for IKEPs of up to fifteen countries. Our experiments show that using lexicographically minimal maximum matchings instead of ones that only minimize the largest deviation from the target allocation (as previously done) may make an IKEP up to 54% more balanced.

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Section: Our Settingmentioning

confidence: 99%

Section: Our Contributionsmentioning

confidence: 99%

“…. , d t , the algorithm calls the polynomial-time algorithm provided by the following lemma from [12] (see also [10]).…”

Section: Computing a Lexicographically Minimal Maximum Matchingmentioning

confidence: 99%

“…Note that Lex-Min terminates as soon as all countries are finished. For a correctness proof and running time analysis of Lex-Min we refer to [12] (see also [10]).…”

Section: Lemma 1 ([12]mentioning

confidence: 99%

Section: Simulations Detailsmentioning

confidence: 99%

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