In this paper the influence of active social agents on the opinions of a certain group over a finite period of time is examined and the changing opinions of group members is analyzed. A social network is considered, the members of which can be divided into passive (agents) and active (players). Players influence agents and try to change their opinion in their preferred direction. There is a conflict between the players, since each of them wants to establish an opinion in the group that is close to his desired one. In the case of such a conflict, the determination of the actions of active members is carried out according to the concept of Nash equilibrium, which reflects a competitive situation between players. Players take into account the dynamics of opinions of agents and act in such a way as to minimize their payoffs.