Abstract

The standard profit-maximizing multi-unit auction intersects the submitted de-mand curve with a preset reservation supply curve, which is determined using the distribution from which the buyers ’ valuations are drawn. However, when this dis-tribution 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 num-berofbuyersgoestoinfinity, and convergence can be substantially faster than with sequential price experimentation. * Department of Economics, Stanford University, Stanford

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