We study the positionality of trigger strategies Nash equilibria $\bar{\sigma }$ for the N-player SCAR games ${\mathrm{\Gamma }}_N(G|s_0,\gamma ,\epsilon )$ (with $N\ge 3$). Our study is exhaustive with respect to types of graphs G, initial states $s_0$ and values of $N,\gamma ,\epsilon$. We conclude that in the majority of cases, profiles $\bar{\sigma }$ are nonpositional. Whenever $\bar{\sigma }$ are positional a key role is played by paths and the ε, γ values (especially whether $\epsilon >0$ or not). A crucial concept in our analysis is the state cop number, which is first introduced in the current paper.

中文翻译：

---

关于SCAR触发策略纳什均衡的位置

我们研究触发策略的位置性纳什均衡$\stackrel{〜}{\sigma }$适用于N玩家SCAR游戏${\mathrm{\Gamma }}_{ñ}（G|s_0，\gamma ，\epsilon ）$ （与 $ñ\ge 3$）。我们对图G的类型，初始状态进行了详尽的研究$s_0$ 和值 $ñ，\gamma ，\epsilon$。我们得出结论，在大多数情况下，$\stackrel{〜}{\sigma }$是无位置的。每当$\stackrel{〜}{\sigma }$在位置上，路径和ε，γ值（尤其是是否$\epsilon >0$或不）。在我们的分析中，一个至关重要的概念是国家警察编号，该编号在本白皮书中首次引入。