One-Step Ahead Optimal Strategy for Opinion Dynamic Games Among Competitive Groups

In the actual social context, the evolution of individual opinions is influenced by the opinions of neighbors within the group and the opinions of individuals outside the group, and the groups are generally competitive. On the other hand, how to choose the optimal strategy to make the individual achieve the predetermined opinion is unclear. In this paper, we study the evolution of opinions among competitive groups by establishing a one-step ahead optimal strategy. Sufficient conditions to ensure the convergence of opinions are given, and furthermore, we give the criteria for determining that individuals achieve the predetermined opinions. Finally, based on Erdös-Rényi network and Grévy's Zebras network, simulation analyses show that the individuals achieve the predetermined opinions by the leaders or players.