  Let $\gamma_g(G)$ be the game domination number of a graph $G$. It is proved
that if ${\rm diam}(G) = 2$, then $\gamma_g(G) \le \left\lceil \frac{n(G)}{2}
\right\rceil- \left\lfloor \frac{n(G)}{11}\right\rfloor$. The bound is
attained: if ${\rm diam}(G) = 2$ and $n(G) \le 10$, then $\gamma_g(G) =
\left\lceil \frac{n(G)}{2} \right\rceil$ if and only if $G$ is one of seven
sporadic graphs with $n(G)\le 6$ or the Petersen graph, and there are exactly
ten graphs of diameter $2$ and order $11$ that attain the bound.
