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Power on digraphs

Author

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  • Peters, Hans

    (QE Math. Economics & Game Theory, RS: GSBE ETBC)

  • Timmer, Judith
  • van den Brink, Rene

Abstract

It is assumed that relations between n players are reflected by a directed graph or digraph. Such a digraph is called invariant if there is an 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 consider- ing additional conditions about the effect of adding a directed link (arc) between two players we single out three different, one parameter families of power indices, reflecting several well-known indices from the literature: Copeland score, β- and apex-type indices.

Suggested Citation

  • Peters, Hans & Timmer, Judith & van den Brink, Rene, 2016. "Power on digraphs," Research Memorandum 019, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2016019
    DOI: 10.26481/umagsb.2016019
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    References listed on IDEAS

    as
    1. Karos, Dominik & Peters, Hans, 2015. "Indirect control and power in mutual control structures," Games and Economic Behavior, Elsevier, vol. 92(C), pages 150-165.
    2. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    3. 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.
    4. 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.
    5. Gambarelli, Gianfranco & Owen, Guillermo, 1994. "Indirect Control of Corporations," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(4), pages 287-302.
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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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    JEL classification:

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

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