Compensation Scheme With Shapley Value  For Multi-Country Kidney Exchange Programmes

Bíró, Péter; Gyetvai, Márton; Klimentova, Xenia; Pedroso, João Pedro; Pettersson, William; Viana, Ana

doi:10.7148/2020-0129

Cited by 11 publications

(27 citation statements)

References 7 publications

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“…There are multiple factors to be analyzed in a global coalition of registries, such as how much additional benefit can be generated for each registry, how the size of registries affects the relative gain of each registry, what are the effects of blood group distribution of pairs in a global coalition. Peter et al have compared two benefit-sharing schemes, which were based on Benefit value and Shapley Value and concluded that both schemes are similar with Shapley value based scheme having lower standard deviation [24].…”

Section: Simulation Planmentioning

confidence: 99%

Analysis of multi-registry kidney exchange program with individual rationality constraints

Verma,

Rangaraj

2020

Preprint

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Kidney exchange programs have been developed to overcome the compatibility challenges for the patient with incompatible donors in kidney transplantation. A registry of such incompatible donor-recipient pairs is created, and compatibility is achieved through the exchange of donors. Singlecenter kidney exchange registries do not have a significant pool size for achieving the full benefits of the kidney exchange program. Thus multi-registry exchange transplants seem to be a natural way forward. There are various challenges in multi-registry exchange programs, such as different constraints for each registry, varying bound on cycle lengths, and data sharing among registries. Researchers have proposed different merging mechanisms with a sequential merger, full merger with fair allocations, and full merger without any restrictions. To form a stable multi-registry sharing mechanism, registries should be individually rational both in the long run as well as in the short run. In this paper, an Integer Programming model for a multi-registry exchange program has been proposed with individual rationality constraints for each registry. A simulation study is conducted to compare the benefits of multi-registry programs with individual registry allocations on Indian data, and multiple analyses have been done. It was concluded that registries with lower arrival rates could benefit 7-9% in terms of the number of transplants and 4-6% in terms of quality of matches in a typical kidney exchange registry. Registry with more hard to match patients will benefit significantly larger than registries with more easy to match patients.

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Section: Simulation Planmentioning

confidence: 99%

Analysis of multi-registry kidney exchange program with individual rationality constraints

Verma,

Rangaraj

2020

Preprint

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“…In their simulations, they allowed 3-way exchanges for four countries and considered the potential and benefit values as target allocations, the latter yielding slightly more balanced solutions. Biró et al [12] compared the benefit value with the Shapley value. In their simulations, for three countries allowing 3-way exchanges, they found that the Shapley value produced smaller deviations from the targets on average.…”

Section: Introductionmentioning

confidence: 99%

“…Biró et al [15] considered credit-based compensation systems from a theoretical point of view. They only allowed for 2-way exchanges but unlike [12,31], with the possibility of having weights for representing transplant utilities. They gave a polynomial-time algorithm for finding a maximum matching that minimized the largest deviation from a target allocation.…”

Section: Introductionmentioning

confidence: 99%

“…Our Contribution. In Section 2 we explain the credit system of [12,15,31] and our settings. We only allow 2-way exchanges (just as [19,20,37], but unlike [12,31]) and do not consider weights (just as [12,31]).…”

Section: Introductionmentioning

confidence: 99%

“…In Section 2 we explain the credit system of [12,15,31] and our settings. We only allow 2-way exchanges (just as [19,20,37], but unlike [12,31]) and do not consider weights (just as [12,31]). In Section 3, we generalize the above polynomial-time result of [15] by giving a polynomial-time algorithm for computing a maximum matching that lexicographically minimizes the country deviations from a given target allocation.…”

Section: Introductionmentioning

confidence: 99%

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Computing Balanced Solutions for Large International Kidney Exchange Schemes

Benedek¹,

Bíró²,

Paulusma³

et al. 2021

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 patientdonor pools. We consider a recent credit system where in each round, countries are given an initial kidney transplant allocation which is adjusted by a credit function yielding a target allocation. The goal is to find a solution in the patient-donor compatibility graph 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 first give a polynomial-time algorithm for computing such matchings. We then perform, for the first time, a computational study for a large number of countries. For the initial allocations we use, besides two easy-to-compute solution concepts, two classical concepts: the Shapley value and nucleolus. These are hard to compute, but by using state-of-the-art software we show that they 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 52% more balanced.

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