  The non-equilibrium statistical mechanics and kinetic theory for a model of a
confined quasi-two-dimensional gas of inelastic hard spheres is presented. The
dynamics of the particles includes an effective mechanism to transfer the
energy injected in the vertical direction to the horizontal degrees of freedom.
The Enskog approximation is formulated and used as the basis to investigate the
temperature and the distribution function of the steady state eventually
reached by the system. An exact scaling of the distribution function of the
system having implications on the form of its moments is pointed out. The
theoretical predictions are compared with numerical results obtained by a
particle simulation method, and a good agreement is found.
