Game theoretic foundations of the Gately power measure for directed networks

TL;DR

This paper introduces a new centrality measure for hierarchical directed networks based on the Gately value from cooperative game theory, linking power distribution to game-theoretic concepts.

Contribution

It develops a novel Gately power measure for directed networks, providing axiomatic foundations and analyzing its relation to existing measures.

Findings

Gately measure can serve as a Core power gauge under certain conditions

The Gately measure is related to the β-measure in network power analysis

An axiomatic characterization of the Gately power measure is provided

Abstract

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 $\beta$-measure, and construct an axiomatisation of the Gately measure.