Incentivized Sequential Testing

We study sequential hypothesis testing when data collection is delegated to a risk-neutral agent who pays for each observation, receives a fixed reward upon rejection, and may quit at any time. The principal chooses an e-process to maximize the probability of rejection before the agent quits. We show that classical growth-optimal e-processes need not be optimal for this objective: tempering the process trades a small loss in evidence growth for reduced fluctuations, which lowers the risk of abandonment and can increase the probability of success. We characterize the abandonment exponent and its unique maximizer within the Gaussian tempered family, and extend the strict improvement to composite nulls under a local stability condition.