  Let ${\rm col_g}(G)$ be the game coloring number of a given graph $G.$ Define
the game coloring number of a family of graphs $\mathcal{H}$ as ${\rm
col_g}(\mathcal{H}) := \max\{{\rm col_g}(G):G \in \mathcal{H}\}.$ Let
$\mathcal{P}_k$ be the family of planar graphs of girth at least $k.$ We show
that ${\rm col_g}(\mathcal{P}_7) \leq 5.$ This result extends a result about
the coloring number by Wang and Zhang {WZ11} (${\rm col_g}(\mathcal{P}_8) \leq
5).$ We also show that these bounds are sharp by constructing a graph $G$ where
$G \in {\rm col_g}(\mathcal{P}_k) \geq 5$ for each $k \leq 8$ such that ${\rm
col_g}(G)=5.$ As a consequence, ${\rm col_g}(\mathcal{P}_k) = 5$ for $k =7,8.$

Combinatorics