Designing the Optimal Menu of Tests
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. By offering a menu, the decision-maker can use the 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 different environments. When the domain of feasible tests contains a most informative test, I obtain conditions under which a dominated test is part of the menu and under which only the most informative test is offered. I also characterise the optimal menu when types are multidimensional or when tests vary in their difficulty.
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