  We look at both the \emph{group labeling lights out game} and the
\emph{neighborhood lights out game}. Our main focus is to determine necessary
and sufficient conditions for when the group labeling lights out game on path
graphs, cycle graphs, and complete bipartite graphs can be won for every
possible initial labeling. In the process of solving this problem, we
demonstrate a new proof for when the neighborhood lights out game on complete
bipartite graphs can be won for every possible initial labeling.
