  In this note we study a new class of alignment models with self-propulsion
and Rayleigh-type friction forces, which describes the collective behavior of
agents with individual characteristic parameters. We describe the long time
dynamics via a new method which allows to reduce analysis from the
multidimensional system to a simpler family of two-dimensional systems
parametrized by a proper Grassmannian. With this method we demonstrate
exponential alignment for a large (and sharp) class of initial velocity
configurations confined to a sector of opening less than $\pi$.
  In the case when characteristic parameters remain frozen, the system governs
dynamics of opinions for a set of players with constant convictions. Viewed as
a dynamical non-cooperative game, the system is shown to possess a unique
stable Nash equilibrium, which represents a settlement of opinions most
agreeable to all agents. Such an agreement is furthermore shown to be a global
attractor for any set of initial opinions.
