  Given a large number of homogeneous players that are distributed across three
possible states, we consider the problem in which these players have to control
their transition rates, while minimizing a cost. The optimal transition rates
are based on the players' knowledge of their current state and of the
distribution of all the other players, and this introduces mean-field terms in
the running and the terminal cost. The first contribution involves a mean-field
game model that brings together macroscopic and microscopic dynamics. We obtain
the mean-field equilibrium associated with this model, by solving the
corresponding initial-terminal value problem. We perform an asymptotic analysis
to obtain a stationary equilibrium for the system. The second contribution
involves the study of the microscopic dynamics of the system for a finite
number of players that interact in a structured environment modeled by an
interaction topology. The third contribution is the specialization of the model
to describe honeybee swarms, virus propagation, and cascading failures in
interconnected smart-grids. A numerical analysis is conducted which involves
two types of cyber-attacks. We simulate in which ways failures propagate across
the interconnected smart grids and the impact on the grids frequencies. We
reframe our analysis within the context of Lyapunov's linearisation method and
stability theory of nonlinear systems and Kuramoto coupled oscillators model.
