Sequential Mechanisms for Evidence Acquisition

We consider optimal mechanisms for inducing agents to acquire costly evidence in a setting where a principal has a good to allocate that all agents want. We show that optimal mechanisms are necessarily sequential in nature and have a threshold structure. Agents with higher costs of obtaining evidence and/or worse distributions of value for the principal are asked for evidence later, if at all. We derive these results using a static optimization problem to characterize the optimal allocation of the good and the probability each agent is asked for evidence, followed by constructing a dynamic mechanism that achieves this outcome.