  A model of self-driven particles similar to the Vicsek model [Phys. Rev.
Lett. 75 (1995) 1226] but with metric-free interactions is studied by means of
a novel Enskog-type kinetic theory. In this model, N particles of constant
speed v0 try to align their travel directions with the average direction of a
fixed number of closest neighbors. At strong alignment a global flocking state
forms. The alignment is defined by a stochastic rule, not by a Hamiltonian. The
corresponding interactions are of genuine multi-body nature. The theory is
based on a Master equation in 3N-dimensional phase space, which is made
tractable by means of the molecular chaos approximation. The phase diagram for
the transition to collective motion is calculated and compared to direct
numerical simulations. A linear stability analysis of a homogeneous ordered
state is performed using the kinetic but not the hydrodynamic equations in
order to achieve high accuracy. In contrast to the regular metric Vicsek-model
no instabilities occur. This confirms previous direct simulations that for
Vicsek-like models with metric-free interactions, there is no formation of
density bands and that the flocking transition is continuous.
