The TRAP protocol solves rational agreement by combining accountable consensus with a one-shot BFTCR finalization phase. We present SNARE (Scalable Nash Agreement via Reward and Exclusion), the adaptation of TRAP to $n=5f{+}1$, and prove $ε$-$(k,t)$-robustness for rational agreement tolerating coalitions up to ${\approx}73\%$ with deposits under $0.5\%$ of the gain. A central finding is that appending a single all-to-all broadcast round with the $4f{+}1$ threshold after predecisions yields $ε$-$(k,t)$-robustness for coalitions up to $3f$ (${\approx}60\%$) without any deposit: we need not model or know the utility function of deviating players, only that they participate in the protocol. These players can be \emph{deceitful} (arbitrary unknown utility), not just rational, and the finalization structure prevents disagreement regardless of their motivation. This observation is protocol-agnostic, applies to any $5f{+}1$ protocol at the cost of one message delay that runs concurrently with the next view, and does not require commit-reveal mechanisms. Above $60\%$, the full baiting mechanism with deposits under $0.5\%$ extends tolerance to ${\approx}73\%$. A second finding is that valid-candidacy, the property preventing reward front-running, holds unconditionally regardless of the quorum threshold, removing both the $n>2(k{+}t)$ and $n>\frac{3}{2}k{+}3t$ constraints from the original TRAP. This retroactively extends the $3f{+}1$ bound from $C<n/2$ to $C<5n/9$. The binding constraint in both models is the winner consensus operating on $2f$ residual players after excluding $3f{+}1$ detected equivocators. We explore avenues for relaxing this limit.

翻译：TRAP协议通过将可问责共识与一次性BFTCR最终确认阶段相结合来解决理性共识问题。我们提出了SNARE（基于奖励与排斥的可扩展纳什共识），即TRAP协议在$n=5f{+}1$场景下的适配方案，并证明了其在存款低于收益0.5%的条件下，可容忍高达约73%的共谋群体，实现理性共识的$ε$-$(k,t)$-鲁棒性。核心发现是：在预处理阶段后附加一轮全向广播轮次并采用$4f{+}1$阈值，可在无需任何存款的条件下，对高达$3f$（约60%）的共谋群体实现$ε$-$(k,t)$-鲁棒性——我们无需建模或知晓偏离协议参与者的效用函数，仅需保证其参与协议即可。这些参与者可以是"欺骗性"的（具有任意未知效用函数），而非仅限于理性参与者，且最终确认结构可无视其动机防止共识分歧。该发现具有协议无关性，适用于任何$5f{+}1$协议，仅需增加一个与下一视图并发运行的消息延迟代价，且无需承诺-揭示机制。当共谋规模超过60%时，存款低于0.5%的完整诱捕机制可将容忍度扩展至约73%。第二个发现是"有效候选资格"——防止奖励抢跑的特性——在任意法定阈值条件下均无条件成立，从而消除了原始TRAP协议中$n>2(k{+}t)$和$n>\frac{3}{2}k{+}3t$两项约束。这使$3f{+}1$模型中的共谋边界从$C<n/2$反向扩展至$C<5n/9$。两个模型的约束瓶颈均在于：排除$3f{+}1$个可检测的欺诈者后，胜者共识需对剩余$2f$个参与方达成。我们探索了放宽该极限的可行路径。