Exploring Network Centrality Through the Lens of Game Theory

We study a class of network games characterized by local complementarities, global congestion effects, and a bounded strategy space. Our first contribution is a representation formula for the Nash equilibrium that expresses players’ equilibrium strategies via a series expansion. Building on this, we define a novel centrality measure derived from the Welfare function evaluated at equilibrium. We then compare our proposed measure with four classical ranking methods and the more recent information centrality, using several well-known datasets.