Nathan Hancart (UCL) 25.01.2023

A decision-maker must accept or reject a privately informed agent. The agent always wants to be accepted, while the decision-maker wants to accept only a subset of types. The decision-maker has access to a set of feasible tests and, prior to making a decision, requires the agent to choose a test from a menu, which is a subset of the feasible tests. By offering a menu, the decision-maker can use the agent's choice as an additional source of information. I characterise the decision-maker's optimal menu for arbitrary type structures and feasible tests. I then apply this characterisation to various environments. When the domain of feasible tests contains a most informative test, I characterise when only the dominant test is offered and when a dominated test is part of the optimal menu. I also characterise the optimal menu when types are multidimensional or when tests vary in their difficulty.