The Bonacich Shapley centrality

In this paper, we develop a new game theoretic network centrality measure based on the Shapley value. To do so, we consider a coalitional game, where the worth of each coalition is the total play in the game introduced in Ballester et al. (2006). We first establish that the game is convex. As a consequence, the Shapley value belongs to the core, which enhances the attractive features of our new centrality measure. Then, we compute the Shapley value for various examples and illustrate some of its properties.