Common mistakes in computing the nucleolus

Guajardo, Mario; Jørnsten, Kurt

doi:10.1016/j.ejor.2014.10.037

Cited by 54 publications

(23 citation statements)

References 18 publications

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“…We propose the computation of the Shapley value for n agents and the nucleolus with a maximum of four agents. As noted by Guajardo and Jörnsten (2015) it is usual to find mistakes in computing the nucleolus, but our results coincide with theirs.…”

Section: Introductionsupporting

confidence: 88%

Enjoying cooperative games: The R package GameTheory

Cano-Berlanga

Gimnez-Gmez

Vilella

2017

Applied Mathematics and Computation

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This paper focuses on cooperative games with transferable utility. We propose the computation of two solutions, the Shapley value for n agents and the nucleolus with a maximum of four agents. The current approach is also focused on conflicting claims problems, a particular case of coalitional games. We provide the computation of the most well-known and used claims solutions: the proportional, the constrained equal awards, the constrained equal losses, the Talmud and the random arrival rules.

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Section: Introductionsupporting

confidence: 88%

Enjoying cooperative games: The R package GameTheory

Cano-Berlanga

Gimnez-Gmez

Vilella

2017

Applied Mathematics and Computation

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“…Due to this reason, its use is not rarely avoided (Krajewska et al 2008;Guo et al 2013) or mistaken (Guajardo and Jörnsten 2015). Several algorithms have been proposed, usually based on linear programming.…”

Section: Linear Programming Algorithmsmentioning

confidence: 97%

Constructive and blocking power in collaborative transportation

2015

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We empirically investigate constructive and blocking power concepts in transportation planning. Our main question is what do these concepts represent in collaborative transportation. We address it by studying cost allocation and coalition structure problems in a real-world case on forest transportation involving eight companies. The potential savings of collaboration in this case account for about 9 %. We find that players more centrally located tend to benefit from the nucleolus allocation, which takes into account only the constructive power. Other methods, which take into account the blocking power, namely the modiclus and the SM-nucleolus, correct the relative importance of the central players with respect to those in more peripheral areas. The blocking power acknowledges that the more peripheral companies, as a block, are still crucial to the collaboration, despite among themselves they have little opportunities for collaboration. Our main conclusion is that incorporating the blocking power as a criterion in a cost sharing rule for collaborative planning in transportation is important specially in the case where the coalition consists of one or few centrally located companies and several peripheral companies. A method based merely on the constructive power might extremely benefit the central companies, hurting the possibilities of sustaining the coalition.

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“…Its computation is somewhat more complicated than the previous methods and several approaches have been proposed in the literature. We refer the reader to [13] for an algorithm based on a sequence of linear programming models and to [16] for several numerical examples. We develop an adapted version of the nucleolus method, referred to as ANM, which uses the same principle, but defines the excess vector only for the 2$jNj coalitions in D\{N} that are relevant to the semicore.…”

Section: Concepts Adapted To Games With Incomplete Characteristic Funmentioning

confidence: 99%