Competition for agents' opinions in small dynamic systems with limited control

This paper explores a competitive opinion dynamic system representing a social network evolving over time. The agents compare their own opinions with the average ones and form new opinions. There are players who control agents' opinions in a social network, and their aims are to make opinions in the society closer to the desired levels over a finite time horizon by minimizing their costs. The feature of this model is that players can influence agents in a limited number of time moments. We show how players can choose the moments of influence from Pareto optimal set on numerical examples. The results of numerical simulations are provided in the work.