Blockchains offer a decentralized and secure execution environment strong enough to host cryptocurrencies, but the state-replication model makes on-chain computation expensive. To avoid heavy on-chain workloads, systems like Truebit and optimistic rollups use challenge-based protocols, performing computations off-chain and invoking the chain only when challenged. This keeps normal-case costs low and, if at least one honest challenger exists, can catch fraud. What has been less clear is whether honest challengers are actually incentivized and a dishonest proposer is properly damaged under the worst case environment. We build a model with a colluding minority, heterogeneous costs, and three ordering modes. We then ask whether two goals can be met together: honest non-loss and fraud deterrence. Our results are clear: in single-winner designs, the incentive design is impossible or limited in scale. By contrast, in multi-winner designs, we obtain simple, explicit conditions under which both goals hold.

翻译：区块链提供了一个去中心化且安全的执行环境，其强度足以承载加密货币，但状态复制模型使得链上计算成本高昂。为了避免繁重的链上工作负载，诸如Truebit和乐观汇总等系统采用挑战型协议，将计算移至链下执行，仅在受到挑战时才调用链上验证。这使正常情况下的成本保持在较低水平，并且只要存在至少一名诚实的挑战者，就能发现欺诈行为。然而，在何种程度上诚实的挑战者确实受到激励，以及不诚实的提议者在最坏情况下是否受到适当的惩罚，这些问题尚不明确。我们构建了一个包含合谋少数派、异质成本和三种排序模式的模型，进而探讨两个目标能否同时实现：诚实参与者的无损失性与欺诈威慑性。我们的结论是明确的：在单一获胜者设计中，激励设计要么不可能实现，要么在规模上受到限制。相比之下，在多重获胜者设计中，我们获得了简单且明确的条件，使得两个目标均能成立。