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

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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.

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Authors and Affiliations

  1. Department of Applied Mathematics II, Industrial and Aeronautic Engineering School of Terrassa, Technical University of Catalonia, Catalonia, Spain

    Rafael Amer & Antonio Magaña

  2. Department of Applied Mathematics III, Engineering School of Manresa, Technical University of Catalonia, Catalonia, Spain

    José Miguel Giménez

  3. EPSEM, Avda. Bases de Manresa 61, 08242, Manresa, Spain

    José Miguel Giménez

Authors
  1. Rafael Amer
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  2. José Miguel Giménez
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  3. Antonio Magaña
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Corresponding author

Correspondence to José Miguel Giménez.

Additional information

Research partially supported by Grant SGR 2009-01029 of the Catalonian Government (Generalitat de Catalunya) and Grant MTM 2009-08037 of the Science and Innovation Spanish Ministry.

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Amer, R., Giménez, J.M. & Magaña, A. Accessibility measures to nodes of directed graphs using solutions for generalized cooperative games. Math Meth Oper Res 75, 105–134 (2012). https://doi.org/10.1007/s00186-011-0378-x

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  • DOI: https://doi.org/10.1007/s00186-011-0378-x

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