  We examine recent high-precision measurements of small-scale quasar
clustering (at $z\sim0.5-2$ on scales of $\sim25~\mathrm{kpc/h}$) from the SDSS
in the context of the MassiveBlackII (MBII) cosmological hydrodynamic
simulation and conditional luminosity function (CLF) modeling. At these high
luminosities ($g < 20.85$ quasars), the MBII simulation volume
($100~\mathrm{cMpc}/h$ comoving boxsize) has only 3 quasar pairs at distances
of $1-4$ Mpc. The black-hole masses for the pairs range between
$M_{bh}\sim1-3\times 10^{9}~M_{\odot}/h$ and the quasar hosts are haloes of
$M_h\sim1-3\times10^{14}~M_{\odot}/h$. Such pairs show signs of recent major
mergers in the MBII simulation. By modeling the central and satellite AGN CLFs
as log-normal and Schechter distributions respectively (as seen in MBII AGNs),
we arrive at CLF models which fit the simulation predictions and observed
luminosity function and the small-scale clustering measured for the SDSS
sample. The small-scale clustering of our mock quasars is well-explained by
central-satellite quasar pairs that reside in $M_h>10^{14}~M_{\odot}/h$ dark
matter haloes. For these pairs, satellite quasar luminosity is similar to that
of central quasars. Our CLF models imply a relatively steep increase in the
maximum satellite luminosity, $L^*_{\mathrm{sat}}$, in haloes of
$M_h>10^{14}~M_{\odot}/h$ with associated larger values of $L^*_{\mathrm{sat}}$
at higher redshift. This leads to increase in the satellite fraction that
manifests itself in an enhanced clustering signal at $\lesssim$ 1 Mpc/h. For
the ongoing eBOSS-CORE sample, we predict $\sim 200-500$ quasar pairs at
$z\sim1.5$ (with $M_h \gtrsim10^{13}~M_{\odot}/h$ and $M_{bh}
\gtrsim10^{8}~M_{\odot}/h$) at $\sim25~\mathrm{kpc}$ scales. Such a sample
would be $\gtrsim10$ times larger than current pair samples.
