Game-theoretic variants of cardinal invariants

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 $\mathrm{add}(\mathsf{n}\mathsf{u}\mathsf{l}\mathsf{l})$. 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.