Coordinated influence on the beliefs of social network members

In this paper, we examine a model of the coordinated influence in a social network in which several its members, called players, can jointly influence the beliefs of other members, called agents, during a finite number of periods. The model is considered as a cooperative dynamic game. The influence of players is expressed by declaring their beliefs which are then considered and weighted by the agents to form their own beliefs. Our goal is to find the declared beliefs 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 allocated using the Shapley value. When we have no information regarding the levels of trust for agents to each other, we estimate these values by means of a centrality measure. Numerical simulation is carried out for a well-known social network of a university karate club and for a lattice often used for modeling spatial networks.