Calibrating Mechanisms with Delayed Evidence

Many mechanisms are designed assuming that payoff-relevant operational characteristics are known when decisions are made, although in practice they may only become assessable from post-action data. We study how delayed, noisy evidence can recover the incentives of such benchmark mechanisms without redesigning them. Our calibrated correction runs the benchmark mechanism using agents' reports and adjusts payoffs ex post according to a statistically calibrated verification score. We show that incentive loss is controlled by two interpretable features of the verifier: its calibration level for truthful reports and its statistical resolution for detecting deviations. This makes explicit the tradeoff between protecting truthful agents from erroneous correction and detecting misreports at finer resolution. Our framework accommodates a broad range of verification procedures, including concentration-based tests and sequential verification via anytime-valid e-processes, and we illustrate it using standard VCG and Myerson resource-allocation benchmarks.