Game theoretic foundations of the Gately power measure for directed networks

08/04/2023

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by   Robert P. Gilles, et al.

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We introduce a new network centrality measure founded on the Gately value for cooperative games with transferable utilities. A directed network is interpreted as representing control or authority relations between players–constituting a hierarchical network. The power distribution of a hierarchical network can be represented through a TU-game. We investigate the properties of this TU-representation and investigate the Gately value of the TU-representation resulting in the Gately power measure. We establish when the Gately measure is a Core power gauge, investigate the relationship of the Gately with the β-measure, and construct an axiomatisation of the Gately measure.