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.

We consider multistage network games with perfect information. At each time instant, a current network structure connecting the players is specified. It is assumed that each edge has some utility value (player’s benefit from being linked to another player), and players can change the network structure at each stage. We propose a method for finding optimal behavior for players in games of this type.

This paper considers a model of opinion dynamics in a social network with two principals, in which the members may affect the opinions of each other and their opinions evolve according to a time-homogeneous Markov chain. We study the existence of a consensus in this network for two types of influence models, namely, when the principals may or may not affect the opinions of each other directly. In addition, we find the values of social network parameters under which a consensus is reached. For the cases without a consensus in its standard definition, we introduce the notion of a consensus of the majority and find the parameter values under which it is reached. Two numerical examples illustrate the obtained theoretical results.