CoBRA: A Universal Strategyproof Confirmation Protocol for Quorum-based Proof-of-Stake Blockchains

The security of many Proof-of-Stake (PoS) payment systems relies on quorum-based State Machine Replication (SMR) protocols. While classical analyses assume purely Byzantine faults, real-world systems must tolerate both arbitrary failures and strategic, profit-driven validators. We therefore study quorum-based SMR under a hybrid model with honest, Byzantine, and rational participants. We first establish the fundamental limitations of traditional consensus mechanisms, proving two impossibility results: (1) in partially synchronous networks, no quorum-based protocol can achieve SMR when rational and Byzantine validators collectively exceed $1/3$ of the participants; and (2) even under synchronous network assumptions, SMR remains unattainable if this coalition comprises more than $2/3$ of the validator set. Assuming a synchrony bound $\Delta$, we show how to extend any quorum-based SMR protocol to tolerate up to $1/3$ Byzantine and $1/3$ rational validators by modifying only its finalization rule. Our approach enforces a necessary bound on the total transaction volume finalized within any time window $\Delta$ and introduces the \emph{strongest chain rule}, which enables efficient finalization of transactions when a supermajority of honest participants provably supports execution. Empirical analysis of Ethereum and Cosmos demonstrates validator participation exceeding the required $5/6$ threshold in over $99$ of blocks, supporting the practicality of our design. Finally, we present a recovery mechanism that restores safety and liveness after consistency violations, even with up to $5/9$ Byzantine stake and $1/9$ rational stake, guaranteeing full reimbursement of provable client losses.