Mathematical Methods of Operations Research

, Volume 75, Issue 1, pp 105–134 | Cite as

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

  • Rafael Amer
  • José Miguel Giménez
  • Antonio Magaña
Original Article

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.

Keywords

Game theory Digraph Accessibility Cooperative game Semivalue 

Mathematics Subject Classification (2000)

91A12 91A43 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Rafael Amer
    • 1
  • José Miguel Giménez
    • 2
    • 3
  • Antonio Magaña
    • 1
  1. 1.Department of Applied Mathematics II, Industrial and Aeronautic Engineering School of TerrassaTechnical University of CataloniaCataloniaSpain
  2. 2.Department of Applied Mathematics III, Engineering School of ManresaTechnical University of CataloniaCataloniaSpain
  3. 3.EPSEMManresaSpain

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