Summary: The game coloring index \(\text{col}_g^\prime(G)\) of a graph \(G\) is the score of the edge marking game (the edge-coloring version of the marking game) on \(G\) when the two players use their best strategy. The game coloring index is at most \(\Delta + 2\) for the class of forests of maximum degree \(\Delta\), denoted \(\mathcal{F}_\Delta\). We prove that \(\text{col}_g^\prime(G) \leq \Delta(G) + 3 a - 1\) for every graph \(G\) of arboricity \(a\), i.e. every graph decomposable into \(a\) forests and we introduce a generalized decomposition of the well-known \((a, d)\)- and \(F(a, d)\)-decompositions to improve this result. In particular, we improve bounds for some planar graphs.