SNARE: A TRAP for Rational Players to Solve Byzantine Consensus in the 5f+1 Model
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| Format: | Preprint |
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2026
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| _version_ | 1866910069700952064 |
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| author | Ranchal-Pedrosa, Alejandro Marsh, Benjamin |
| author_facet | Ranchal-Pedrosa, Alejandro Marsh, Benjamin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23458 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | SNARE: A TRAP for Rational Players to Solve Byzantine Consensus in the 5f+1 Model Ranchal-Pedrosa, Alejandro Marsh, Benjamin Computer Science and Game Theory Distributed, Parallel, and Cluster Computing 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. |
| title | SNARE: A TRAP for Rational Players to Solve Byzantine Consensus in the 5f+1 Model |
| topic | Computer Science and Game Theory Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2603.23458 |