  (Abridged) We make predictions for the pairwise velocity dispersion (PVD) of
galaxies with models that are constrained to match the projected correlation
function and luminosity function of galaxies in the Two-Degree Field Galaxy
Redshift Survey (2dFGRS). We use these data to constrain the halo occupation
distribution (HOD), then calculate the PVD by populating the halos of a high
resolution N-body simulation. We examine the luminosity and scale dependence of
the predicted PVD. At r<1 Mpc/h and r>3 Mpc/h, we find that the PVD decreases
with increasing galaxy luminosity. This result is mostly driven by the fraction
of satellite galaxies f_sat, which is well-constrained by the correlation
function. We find f_sat~25% for galaxies fainter than L_star, while for
brighter galaxies the satellite fraction rapidly declines, creating the
decrease in the PVD with luminosity. At r=1 Mpc/h, the PVD has no dependence on
luminosity because satellite galaxies dominate the statistics for all objects.
Recent measurements of the PVD in Fourier space using the "dispersion model"
have reported a strong decline in PVD with increasing luminosity at k=1 h/Mpc.
We test this method with our HOD models, finding that there is no consistent
comparison between the PVD at a given k and the true dispersion at a given
value of r. This results in a luminosity dependence in k-space that is stronger
than in configuration space. The luminosity dependence of the HOD results in
Fourier space are consistent with those measured at k=1 h/Mpc; thus the recent
measurements of the PVD are fully explainable in the context of halo occupation
models. The normalization of the PVD is lower than predicted by our fiducial
model, and reproducing it requires a lower value of Omega_m (~0.2 instead of
0.3), a lower value of sigma_8 (~0.7 instead of 0.9), or strong velocity bias.
