Let γg(G) be the game domination number of a graph G. It is proved
that if diam(G)=2, then γg(G)≤⌈2n(G)⌉−⌊11n(G)⌋. The bound is
attained: if diam(G)=2 and n(G)≤10, then γg(G)=⌈2n(G)⌉ if and only if G is one of seven
sporadic graphs with n(G)≤6 or the Petersen graph, and there are exactly
ten graphs of diameter 2 and order 11 that attain the bound