Abstract
m identical objects are to be sold in a multiple-bid auction where the m highest bids are accepted. An efficient private value auction must induce an identical transformation of all values of the bidders into bids. (In a common value auction the problem of allocative efficiency disappears.) The pricing rule has to be an additively separable function of the bids.Under the condition that a pricing rule is efficient, monotone, and reciprocitive (a bidder has to pay only for the units received) it has to obey certain restrictions. These restrictions are not met by the pricing rules found in large-scale auctions as the British electricity auction and the auctions organized by the American Treasury Department and by the German Bundesbank. If the pricing rule is “simple” the Vickrey rule and trivial transformations of the Vickrey rule are the only efficient pricing rules.
I would like to thank Werner Güth for helpful comments on a previous version of this paper.
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Bolle, F. (1997). Necessary Conditions for Efficient Multiple-Bid Auctions. In: Nau, R., Grønn, E., Machina, M., Bergland, O. (eds) Economic and Environmental Risk and Uncertainty. Theory and Decision Library, vol 35. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1360-3_9
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