On Influence and Power Indices

Abstract. In the paper, we introduce and study influence indices of a coalition on a player in a social network. It is assumed that each player has an inclination to say ‘yes ’ or ‘no ’ which, due to influence of other players, may be different from the decision of the player. The point of departure here is the concept of the Hoede-Bakker index- the notion which computes the overall decisional ‘power ’ of a player in a social network. The main drawback of the Hoede-Bakker index is that it hides the actual role of the influence function, analyzing only the final decision in terms of success and failure. In this paper, we propose an improvement which fully takes into account the mutual influence among players. A global index which distinguishes an influence degree from a ‘power ’ index is analyzed, and weighted influence indices are defined. We consider different influence functions and study their properties. JEL Classification: C7, D