Large-Scale Group Opinion Evolution With Coexistence of Influential Individuals and Strongly Organized Groups Based on Mean Field Games

With the vigorous development of online media, the prevalence of key opinion leaders and water armies has led to unexpected evolutions of users' opinions. Therefore, it is valuable and interesting to investigate the opinion evolution problem for large-scale groups with the coexistence of influential individuals and strongly organized groups. For the above problem, based on the mean-field game theory, this article innovatively proposes a multi-leader multi-population-follower Stackelberg mean field game (MLMPF-SMFG) model to describe the opinion evolution scenario, in which influential individuals are regarded as leaders, normal and strongly organized groups are regarded as follower populations. Moreover, for generality, the types of strongly organized individuals are classified into three typical types: propagandists, spies, and neutrals. Then, the optimal strategies are derived via the adjoint method and solved by forward–backward stochastic differential equations. Sufficient conditions for the existence and uniqueness of the Stackelberg equilibrium (SE) are given, and the approximate SE of the finite system is proven. Finally, simulation experiments on the opinion evolutions of two influential individuals and two ordinary groups are performed to demonstrate the feasibility and effectiveness of the proposed MLMPF-SMFG model.