  We analyze the domination game, where two players, Dominator and Staller,
construct together a dominating set M in a given graph, by alternately
selecting vertices into M. Each move must increase the size of the dominated
set. The players have opposing goals: Dominator wishes M to be as small as
possible, and Staller has the opposite goal. Kinnersley, West and Zamani
conjectured that when both players play optimally on an isolate-free forest,
there is a guaranteed upper bound for the size of the dominating set that
depends only on the size n of the forest. This bound is 3n/5 when the first
player is Dominator, and (3n+2)/5 when the first player is Staller. The
conjecture was proved for specific families of forests by Kinnersley et al. and
later extended by Bujtas. Here we prove it for all isolate-free forests, by
supplying an algorithm for Dominator that guarantees the desired bound.
