Digraph competitions and cooperative games
type: Item
instance of: scholarly article
title: Digraph competitions and cooperative games
zbMATH Open document ID: 1112.91007
DOI: 10.1023/A:1024162419357
author: René van den Brink
author: Peter Borm
published in: Theory and Decision
publication date: 2003-08-20T00:00:00Z
review text: The authors consider the model of a fixed finite set \(N\) of nodes with domination structure described by a directed graph \(D \subset N \times N\) (\textit{digraph competition}). The purpose of the paper is to propose a new procedure determining the power of each node. To this end, a cooperative TU-game (\textit{digraph game}) is defined, strictly related with a digraph \(D\). Next the Shapley value, the core and a selectope of a digraph game are found and discussed. Also some remarks about possible weighted digraph competitions are given. The results of the paper are illustrated with two examples of digraph competitions where the Shapley value is applied to evaluate the strength of posistions. The first one analyzes the situation of the UFFA European Soccer Championship (EURO 2000). The second example discusses an application to the ranking of alternatives in social choice theory.
reviewed by: Tadeusz Radzik
Mathematics Subject Classification ID: 91A12
Mathematics Subject Classification ID: 91A43
Mathematics Subject Classification ID: 91A06
Mathematics Subject Classification ID: 91B14
zbMATH DE Number: 1968049
zbMATH Keywords: digraph competition
zbMATH Keywords: cooperative TU-game
zbMATH Keywords: Shapley value
zbMATH Keywords: core
zbMATH Keywords: marginal vector
zbMATH Keywords: selectope vector
zbMATH Keywords: simple score vector
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1968049