  Electron localization and polaron mobility in oxygen deficient as well as Li
doped monoclinic tungsten trioxide have been studied. We show that small
polarons formed in the presence of oxygen vacancy prefer the bipolaronic
$W^{5+}- W^{5+}$ configuration whereas the $W^{6+}- W^{4+}$ configuration is
found to be metastable. Our calculations suggest that bipolarons are tightly
bound by the vacancy and therefore largely immobile. On the contrary, polarons
formed as a result of Li intercalation can be mobile, the activation energy for
polaron jumping in this case varies between 98 and 124 meV depending on the
crystallographic direction. The formation of $W^{5+}- W^{5+}$ bipolarons in
$Li-WO_{3}$ is possible. When situated along $[001]$ the bipolaronic
configuration is 8 meV lower in energy than two separate $W^{5+}$ polarons.
