Information Design in Allocation with Costly Verification

A principal who values an object allocates it to one or more agents. Agents learn private information (signals) from an information designer about the allocation payoff to the principal. Monetary transfer is not available but the principal can costly verify agents' private signals. The information designer can influence the agents' signal distributions, based upon which the principal maximizes the allocation surplus. An agent's utility is simply the probability of obtaining the good. With a single agent, we characterize (i) the agent-optimal information, (ii) the principal-worst information, and (iii) the principal-optimal information. Even though the objectives of the principal and the agent are not directly comparable, we find that any agent-optimal information is principal-worst. Moreover, there exists a robust mechanism that achieves the principal's payoff under (ii), which is therefore an optimal robust mechanism. Many of our results extend to the multiple-agent case; if not, we provide counterexamples.