Common Mistakes in Computing the Nucleolus

Guajardo, Mario; Jørnsten, Kurt

doi:10.2139/ssrn.2425596

Cited by 3 publications

(2 citation statements)

References 23 publications

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“…This game has two minimum-sum integer representations, where the quota is 99 and the weight vectors are w 1 = (38, 31,31,28,23,12,11,8,6,5,3,1) and, respectively, w 2 = (37, 31,31,28,23,12,11,8,7,5,3,1). The weight vectors differ with respect to two non-symmetric players (i.e., players 1 and 9).…”

Section: Discussionmentioning

confidence: 99%

The Integer Nucleolus of Directed Simple Games: A Characterization and an Algorithm

Wolff

2017

Games

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Abstract:We study the class of directed simple games, assuming that only integer solutions are admitted; i.e., the players share a resource that comes in discrete units. We show that the integer nucleolus-if nonempty-of such a game is composed of the images of a particular payoff vector under all symmetries of the game. This payoff vector belongs to the set of integer imputations that weakly preserve the desirability relation between the players. We propose an algorithm for finding the integer nucleolus of any directed simple game with a nonempty integer imputation set. The algorithm supports the parallel execution of multiple threads in a computer application. We also consider the integer prenucleolus and the class of directed generalized simple games.

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Section: Discussionmentioning

confidence: 99%

The Integer Nucleolus of Directed Simple Games: A Characterization and an Algorithm

Wolff

2017

Games

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“…Common mistakes to avoid are pointed out in Guajardo and Jörnsten (2015). The procedure (P NUC ) we use solves a sequence of optimization problems.…”

Section: Nucleolusmentioning

confidence: 99%

Incitements for transportation collaboration by cost allocation

Dahlberg

Engevall

Göthe‐Lundgren

et al. 2018

Cent Eur J Oper Res

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In this paper, we focus on how cost allocation can be used as a means to create incentives for collaboration among companies, with the aim of reducing the total transportation cost. The collaboration is assumed to be preceded by a simultaneous invitation of the companies to collaborate. We make use of concepts from cooperative game theory, including the Shapley value, the Nucleolus and the EPM, and develop specific cost allocation mechanisms aiming to achieve large collaborations among many companies. The cost allocation mechanisms are tested on a case study that involves transportation planning activities. Although the case study is from a specific transportation sector, the findings in this paper can be adapted to collaborations in other types of transportation planning activities. Two of the cost allocation mechanisms ensure that any sequence of companies joining the collaboration represents a complete monotonic path, that is, any sequence of collaborating companies is such that the sequences of allocated costs are non-increasing for all companies.

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