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Power on digraphs

Author

Listed:
  • Hans Peters
  • Judith Timmer
  • Rene van den Brink

Abstract

It is assumed that relations between n players are represented by a directed graph or digraph. Such a digraph is called invariant if there is a link (arc) between any two players between whom there is also a directed path. We characterize a class of power indices for invariant digraphs based on four axioms: Null player, Constant sum, Anonymity, and the Transfer property. This class is determined by 2n – 2 parameters. By considering additional conditions about the effect of adding a directed link between two players, we single out three different, one-parameter families of power indices, reflecting several well-known indices from the literature: the Copeland score,and apex type indices.

Suggested Citation

  • Hans Peters & Judith Timmer & Rene van den Brink, 2016. "Power on digraphs," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 26(2), pages 107-125.
    • Handle: RePEc:wut:journl:v:2:y:2016:p:107-125:id:1224
    DOI: 10.5277/ord160207
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    References listed on IDEAS

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    1. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    2. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    3. Gambarelli, Gianfranco & Owen, Guillermo, 1994. "Indirect Control of Corporations," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(4), pages 287-302.
    4. Karos, Dominik & Peters, Hans, 2015. "Indirect control and power in mutual control structures," Games and Economic Behavior, Elsevier, vol. 92(C), pages 150-165.
    5. Dubey, Pradeep & Einy, Ezra & Haimanko, Ori, 2005. "Compound voting and the Banzhaf index," Games and Economic Behavior, Elsevier, vol. 51(1), pages 20-30, April.
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    Cited by:

    1. Qianqian Kong & Hans Peters, 2021. "An issue based power index," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 23-38, March.

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    More about this item

    Keywords

    digraph; power index; transfer property; link addition;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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