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Power on digraphs

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PETERS H., TIMMER J., VAN DEN BRINK R.
Operations Research and Decisions
|
2016
|
vol. 26
|
issue 2
107-125
EN
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.
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