doi:10.1016/j.peva.2007.02.002
Copyright © 2007 Elsevier Ltd All rights reserved.
Performance of the Vickrey auction for digital goods under various bid distributions
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M. Naldi
, a,
and G. D’Acquistoa, 
aUniversità di Roma “Tor Vergata”, Dip. di Informatica Sistemi Produzione (DISP), Via del Politecnico 1, 00133 Roma, Italy
Received 1 October 2005;
revised 26 July 2006;
accepted 3 February 2007.
Available online 8 February 2007.
Abstract
The generalized Vickrey auction is analysed as a mechanism for setting prices of digital goods. A selection of models of the bidders’ behaviour (embodied by the probability distribution of their bids’ values) are employed to derive the optimal auctioneer’s choice as to the number of items to sell. The satisfaction levels of both the auctioneer and the bidders are taken into account through the evaluation of the expected revenues, the percentage of winning bidders and their aggregated utilities under each of the probabilistic scenarios considered.
Keywords: Auctions; Vickrey; Digital goods; Bid distributions
Fig. 1. Metrics for the bidders’ satisfaction.
Fig. 2. Influence of the number of accepted bids on the revenues in the uniform case.
Fig. 3. Optimal percentage of accepted bids in the uniform case.
Fig. 4. Efficiency of the single price strategy in the uniform case.
Fig. 5. Influence of the number of accepted bids on the revenues in the triangular case.
Fig. 6. Optimal percentage of accepted bids in the triangular case.
Fig. 7. Efficiency of the single price strategy in the triangular case.
Fig. 8. Satisfied utility margin for the triangular distribution.
Fig. 9. Influence of the number of accepted bids on the revenues in the Gaussian case.
Fig. 10. Optimal percentage of accepted bids in the Gaussian case.
Fig. 11. Efficiency of the single price strategy in the Gaussian case.
Fig. 12. Satisfied utility margin for the Gaussian distribution.
Fig. 13. Influence of the number of accepted bids on the revenues in the exponential case (N=100).
Fig. 14. Number of accepted bids on the revenues in the Pareto case (c=1,N=100).
Fig. 15. Revenue loss when the actual distribution is uniform.
Fig. 16. Revenue loss when the actual distribution is triangular.
Fig. 17. Revenue loss when the actual distribution is Gaussian.
Fig. 18. A priori loss for the symmetrical probability models.
Fig. 19. A priori loss for the exponential and Pareto models.

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