We study the positionality of \emph{trigger strategies} Nash equilibria $\overlineσ$ for the $N$-player SCAR games $Γ_{N}(G|s_{0},γ,\varepsilon)$ (with $N\geq3$). Our study is exhaustive with respect to types of graphs $G$, initial states $s_{0}$ and values of $N,γ,\varepsilon$. We conclude that in the majority of cases, profiles $\overlineσ$ are nonpositional. Whenever $\overlineσ$ are positional a key role is played by paths and the $\varepsilon$, $γ$ values (especially whether $\varepsilon>0$ or not). A crucial concept in our analysis is the \emph{state cop number}, which is first introduced in the current paper.