How to Sequence Questions.

Résumé

We consider a communication game between an agent (the informed party) and a principal (the decision maker). The agent privately observes a set of signals informative about the state and the principal asks the agent a sequence of questions about the signals. A question is a set of signals from which the agent chooses one to disclose. Questions asked can be history-dependent. We consider cherry-picking equilibria and characterize equilibrium sequence of questions. If the reverse hazard rate of the signals is log-submodular, then the principal asks a sequence of narrow questions. If the reverse hazard rate of the signals is log-supermodular, then the principal asks a sequence of progressively narrower questions starting with a broad question.