Topological games and productively countably tight spaces

The two main results of this work are the following: if a space X   is such that player II has a winning strategy in the game G1(Ωx,Ωx)G1(Ωx,Ωx) for every x∈Xx∈X, then X   is productively countably tight. On the other hand, if a space is productively countably tight, then S1(Ωx,Ωx)S1(Ωx,Ωx) holds for every x∈Xx∈X. With these results, several other results follow, using some characterizations made by Uspenskii and Scheepers.