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Accessibility measures to nodes of directed graphs using solutions for generalized cooperative games

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  • Rafael Amer
  • José Giménez
  • Antonio Magaña

Abstract

The aim of this paper consists of constructing accessibility measures to the nodes of directed graphs using methods of Game Theory. Since digraphs without a predefined game are considered, the main part of the paper is devoted to establish conditions on cooperative games so that they can be used to measure accessibility. Games that satisfy desirable properties are called test games. Each ranking on the nodes is then obtained according to a pair formed by a test game and a solution defined on cooperative games whose utilities are given on ordered coalitions. The solutions proposed here are extensions of the wide family of semivalues to games in generalized characteristic function form. Copyright Springer-Verlag 2012

Suggested Citation

  • Rafael Amer & José Giménez & Antonio Magaña, 2012. "Accessibility measures to nodes of directed graphs using solutions for generalized cooperative games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(1), pages 105-134, February.
    • Handle: RePEc:spr:mathme:v:75:y:2012:i:1:p:105-134
    DOI: 10.1007/s00186-011-0378-x
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    References listed on IDEAS

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