Hans Peters*, Judith Timmer, Rene van den Brink

*Corresponding author for this work

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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, beta- and apex type indices.
Original languageEnglish
Pages (from-to)107-125
JournalOperations Research and Decisions
Issue number2
Publication statusPublished - 2016


  • digraph
  • power index
  • transfer property
  • link addition

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