Computer Science - Cryptography and Security, Computer Science - Computational Engineering, Finance, and Science, Computer Science - Computer Science and Game Theory, K.6.5, C.2.2, F.2

Optimistic Rollups (ORUs) significantly enhance blockchain scalability but inherently suffer from the verifier's dilemma, particularly concerning validator attentiveness. Current systems lack mechanisms to proactively ensure validators are diligently monitoring L2 state transitions, creating a vulnerability where fraudulent states could be finalized. This paper introduces the Randomized Attention Test (RAT), a novel L1-based protocol designed to probabilistically challenge validators in ORUs, thereby verifying their liveness and computational readiness. Our game-theoretic analysis demonstrates that an Ideal Security Equilibrium, where all validators are attentive and proposers are honest, can be achieved with RAT. Notably, this equilibrium is attainable and stable with relatively low economic penalties (e.g., under $1000) for non-responsive validators and a low attention test frequency (e.g., under 1% per epoch). RAT thus provides a crucial, practical mechanism to enforce validator diligence, fortifying the overall security and integrity of ORU systems with minimizing additional costs.