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Games 2017, 8(1), 16; doi:10.3390/g8010016

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

Department of Economics, University of Fribourg, 1700 Fribourg, Switzerland
Academic Editors: Luca Dall’Asta and Paolo Pin
Received: 16 November 2016 / Revised: 20 January 2017 / Accepted: 7 February 2017 / Published: 28 February 2017
(This article belongs to the Special Issue Combinatorial Optimization and Games)
View Full-Text   |   Download PDF [346 KB, uploaded 28 February 2017]

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. View Full-Text
Keywords: integer nucleolus; integer prenucleolus; desirability relation; simple games; JEL Classification; C63; C71; D72 integer nucleolus; integer prenucleolus; desirability relation; simple games; JEL Classification; C63; C71; D72
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Wolff, R. The Integer Nucleolus of Directed Simple Games: A Characterization and an Algorithm. Games 2017, 8, 16.

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