Competing Incentives in Sequential Sampling Rules

We describe a framework in which two parties have competing objectives in estimating the mean performance of a stochastic system through sequential sampling. A “regulator” is interested in obtaining a correct measurement with an acceptable probability level, while the “stakeholder” in the project is interested in minimizing the cost associated with the output performance measure and the sampling cost. We demonstrate how the stakeholder can choose an optimal sampling rule to minimize their costs when they have private information which is not shared with the regulator. We further suggest how the regulator can choose a key controllable parameter of the optimal sampling rule in order to asymptotically approach a fair result for both parties.