Allocation With Correlated Information: Too Good to Be True

A principal can allocate an indivisible good to an agent. The agent privately learns the value of the good while the principal privately learns the cost. Value and cost are correlated. The agent wants to have the good in any case. The principal wants to allocate whenever the value exceeds the cost. She cannot use monetary transfers to screen the agent. I study how the principal utilizes her information in the optimal mechanism: when the correlation is negative, she bases her decision only on the costs, and when the correlation is positive, she screens the agent. To this end, she forgoes her best allocation opportunities: when the agent reports high valuations but her own costs are low. Under positive correlation, these realizations are unlikely; the principal will find them too good to be true. In contrast to standard results, this optimal mechanism may not allocate to a higher value agent with higher probability. I discuss applications to intra-firm allocations, task-delegation, and industry self-regulation.