Construction with opposition: cardinal invariants and games

We consider several game versions of the cardinal invariants t , u and a . We show that the standard proof that parametrized diamond principles prove that the cardinal invariants are small actually shows that their game counterparts are small. On the other hand we show that t < t Builder and u < u Builder are both relatively consistent with ZFC, where t Builder and u Builder are the principal game versions of t and u , respectively. The corresponding question for a remains open.