Key player identification: a note on weighted connectivity games and the Shapley value

The use of graph theory in social network analysis to identify the most important actors is well-known. More recently game theory has also been applied to measure centrality as variation in the power due to the social structure. Here we present such a solution concept from cooperative game theory, the Shapley value, to identify key players engaged in a network. The communication structure among the players is modeled by use of the so-called connectivity game. We analyze standard networks representative of covert organizations and present results on the centrality of players organized according to an a-symmetric path structure. In addition we present an analysis of a weighted connectivity game in which the worth of coalitions not only depends on their interaction structure but also on exogenous factors.