  In this paper a relationship is established between the domination game and
minimal edge cuts. It is proved that the game domination number of a connected
graph can be bounded above in terms of the size of minimal edge cuts. In
particular, if $C$ a minimum edge cut of a connected graph $G$, then
$\gamma_g(G) \le \gamma_g(G\setminus C) + 2\kappa'(G)$. Double-Staller graphs
are introduced in order to show that this upper bound can be attained for
graphs with a bridge. The obtained results are used to extend the family of
known traceable graphs whose game domination numbers are at most one-half their
order. Along the way two technical lemmas, which seem to be generally
applicable for the study of the domination game, are proved.
