Finding and verifying the nucleolus of cooperative games

Benedek, Márton; Fliege, Jörg; Nguyen, Tri-Dung

doi:10.1007/s10107-020-01527-9

Cited by 12 publications

(5 citation statements)

References 24 publications

(59 reference statements)

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“…A challenging part of our project was to compute the nucleolus of generalized matching games consisting of up to fifteen countries. For this we used the state-of-the-art Lexicographical Descent method of [9]. Future Research.…”

Section: Discussionmentioning

confidence: 99%

“…For the Shapley value, we were still able to implement a naive approach relying directly on (1). However, computing the nucleolus of a generalized matching game is highly nontrivial for the number of countries we consider: we had to use the Lexicographical Descent method of [9], which is the state-of-the-art method in nucleolus computation. 7 Solutions.…”

Section: The Simulationsmentioning

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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Section: Discussionmentioning

confidence: 99%

Section: The Simulationsmentioning

confidence: 99%

Computing Balanced Solutions for Large International Kidney Exchange Schemes

Benedek¹,

Bíró²,

Paulusma³

et al. 2021

Preprint

Self Cite

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show abstract

“…However, a naive approach for computing the nucleolus of a partitioned matching games is not possible for the high number of countries we consider. We therefore use the Lexicographical Descent method of [13], which is the state-of-the-art method in nucleolus computation. 10 Solutions.…”

Section: Simulations Detailsmentioning

confidence: 99%

“…A challenging part of our project was to compute the nucleolus of partitioned matching games consisting of up to fifteen countries. For this we used the state-of-the-art Lexicographical Descent method of [13].…”

Section: Convexity and Quasibalancednessmentioning

confidence: 99%

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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“…To compute the target numbers for each of the countries, Benedek et al (2022) used two solution concepts, the benefit value and the contribution value, which can be computed in linear time, 2 and two solution concepts, the Shapley value and the nucleolus, which in general take exponential time to compute; in particular, they employed the state-of-the-art method (Benedek et al, 2021) for computing the nucleolus. From their simulations, the Shapley value yielded the best results.…”

Section: Matching Games and Generalizationsmentioning

confidence: 99%

The Complexity of Matching Games: A Survey

Benedek,

Biro,

Johnson

et al. 2023

jair

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Matching games naturally generalize assignment games, a well-known class of cooperative games. Interest in matching games has grown recently due to some breakthrough results and new applications. This state-of-the-art survey provides an overview of matching games and extensions, such as b-matching games and partitioned matching games; the latter originating from the emerging area of international kidney exchange. In this survey we focus on computational complexity aspects of various game-theoretical solution concepts, such as the core, nucleolus and Shapley value, when the input is restricted to a matching game or one of its variants.

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Finding and verifying the nucleolus of cooperative games

Cited by 12 publications

References 24 publications

Computing Balanced Solutions for Large International Kidney Exchange Schemes

Computing Balanced Solutions for Large International Kidney Exchange Schemes

Computing Balanced Solutions for Large International Kidney Exchange Schemes

The Complexity of Matching Games: A Survey

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