Optimal Pricing Mechanisms with Unknown Demand

Abstract

The standard profit-maximizing multiunit auction intersects the submitted demand curve with a preset reservation supply curve, which is determined using the distribution from which the buyers' valuations are drawn. However, when this distribution is unknown, a preset supply curve cannot maximize monopoly profits. The optimal pricing mechanism in this situation sets a price for each buyer on the basis of the demand distribution inferred statistically from other buyers' bids. The resulting profit converges to the optimal monopoly profit with known demand as the number of buyers goes to infinity, and convergence can be substantially faster than with sequential price experimentation.