Bandwagon effect in mean field games

This paper provides a mean-field game theoretic model of the bandwagon effect in social networks. The latter phenomenon can be observed whenever individuals tend to align their own opinions to a mainstream opinion. The contribution is three-fold. First, we provide a mean-field games framework that describes the opinion propagation under local interaction. Second, we establish mean-field equilibrium strategies in the case where the mainstream opinion is stationary. Such strategies are shown to have a threshold structure. Third, we study conditions under which a given opinion distribution is stationary if agents implement optimal non-idle and threshold strategies