Mean-Field Game Modeling the Bandwagon Effect with Activation Costs

This paper provides a mean‐field game theoretic model of the bandwagon effect in social networks. This effect can be observed whenever individuals tend to align their own opinions to a mainstream opinion. The contribution is threefold. First, we describe the opinion propagation as a mean‐field game with local interactions. Second, we establish mean‐field equilibrium strategies in the case where the mainstream opinion is constant. Such strategies are shown to have a threshold structure. Third, we extend the use of threshold strategies to the case of time‐varying mainstream opinion and study the evolution of the macroscopic system.