  The redshift-space distortion (RSD) in the observed distribution of galaxies
is known as a powerful probe of cosmology. Observations of large-scale RSD have
given tight constraints on the linear growth rate of the large-scale structures
in the universe. On the other hand, the small-scale RSD, caused by galaxy
random motions inside clusters, has not been much used in cosmology, but also
has cosmological information because universes with different cosmological
parameters have different halo mass functions and virialized velocities. We
focus on the projected correlation function $w(r_p)$ and the multipole moments
$\xi_l$ on small scales ($1.4$ to $30\ h^{-1}\rm{Mpc}$). Using simulated galaxy
samples generated from a physically motivated most bound particle (MBP)-galaxy
correspondence scheme in the Multiverse Simulation, we examine the dependence
of the small-scale RSD on the cosmological matter density parameter $\Omega_m$,
the satellite velocity bias with respect to MBPs, $b_v^s$, and the
merger-time-scale parameter $\alpha$. We find that $\alpha=1.5$ gives an
excellent fit to the $w(r_p)$ and $\xi_l$ measured from the SDSS-KIAS value
added galaxy catalog. We also define the ``strength'' of Fingers-of-God as the
ratio of the parallel and perpendicular size of the contour in the two-point
correlation function set by a specific threshold value and show that the
strength parameter helps constraining $(\Omega_m, b_v^s, \alpha)$ by breaking
the degeneracy among them. The resulting parameter values from all measurements
are $(\Omega_m,b_v^s)=(0.272\pm0.013,0.982\pm0.040)$, indicating a slight
reduction of satellite galaxy velocity relative to the MBP. However,
considering that the average MBP speed inside haloes is $0.94$ times the dark
matter velocity dispersion, the main drivers behind the galaxy velocity bias
are gravitational interactions, rather than baryonic effects.
