Optimal Pricing Mechanisms with Unknown Demand

The standard profit-maximizing multi-unit auction can be represented as the Vickrey-Groves-Clarke mechanism in which the seller manipulates his reservation supply curve. The optimal supply curve depends on 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 to 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 faster than with sequential price experimentation