We investigate game-theoretic variants of cardinal invariants of the continuum. The invariants we treat are the reaping number $\mathfrak{ r}$, the bounding number $\mathfrak{ b}$, the dominating number $\mathfrak{ d}$, and the additivity number of the null ideal $\operatorname{ add}(\mathsf{ null})$. We also consider games, called tallness games, defined according to ideals on $\omega$ and characterize that each of Player I and Player II has a winning strategy.
Categories: math.LO