  In the m-\emph{Eternal Domination} game, a team of guard tokens initially
occupies a dominating set on a graph $G$. An attacker then picks a vertex
without a guard on it and attacks it. The guards defend against the attack: one
of them has to move to the attacked vertex, while each remaining one can choose
to move to one of his neighboring vertices. The new guards' placement must
again be dominating. This attack-defend procedure continues eternally. The
guards win if they can eternally maintain a dominating set against any sequence
of attacks, otherwise, the attacker wins.
  The m-\emph{eternal domination number} for a graph $G$ is the minimum amount
of guards such that they win against any attacker strategy in $G$ (all guards
move model). We study rectangular grids and provide the first known general
upper bound on the m-eternal domination number for these graphs. Our novel
strategy implements a square rotation principle and eternally dominates $m
\times n$ grids by using approximately $\frac{mn}{5}$ guards, which is
asymptotically optimal even for ordinary domination.
