Coordinated Influence on the Opinions of Social Network Members

This paper studies a model of coordinated influence in a social network in which several members, called players, can jointly affect the opinions of other members, called agents, during a finite period of time. The model is treated as a cooperative dynamic game. The influence of players is expressed by declaring their opinions which are then considered and weighted by the agents to form their own opinions. The goal is to find the declared opinions of players focusing only on associated costs as well as on the average deviation of agents beliefs from the desired ones. Under coordination, the total costs of players are distributed using the Shapley value. If there is no information about the degrees of trust of agents to each other, these degrees are estimated using a centrality measure. Numerical simulation is performed for a well-known social network of a university karate club and for a lattice graph often used for modeling of spatial networks.