Optimal mechanism design when both allocative inefficiency and expenditure inefficiency matter

We characterize the structure of optimal assignment rules when both allocative inefficiency and expenditure inefficiency (e.g., rent-seeking) are present. We find that the optimal structure critically depends on how the hazard rate of the value distribution behaves, and that it is often optimal to use probabilistic assignment rules so that the winner of the object is not always the one with the highest valuation. We also find that the inefficiency of the optimal assignment rule decreases as the variability of the value distribution increases.