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Fernando Beltrán, Natalia Santamaría, "A measure of the variability of revenue in auctions: A look at the revenue equivalence theorem", Advances in Decision Sciences, vol. 2006, Article ID 027417, 14 pages, 2006. https://doi.org/10.1155/JAMDS/2006/27417
A measure of the variability of revenue in auctions: A look at the revenue equivalence theorem
One not-so-intuitive result in auction theory is the revenue equivalence theorem, which states that as long as an auction complies with some conditions, it will on average generate the same revenue to an auctioneer as the revenue generated by any other auction that complies with them. Surprisingly, the conditions are not defined on the payment rules to the bidders but on the fact that the bidders do not bid below a reserve value—set by the auctioneer—the winner is the one with the highest bidding and there is a common equilibrium bidding function used by all bidders. In this paper, we verify such result using extensive simulation of a broad range of auctions and focus on the variability or fluctuations of the results around the average. Such fluctuations are observed and measured in two dimensions for each type of auction: as the number of auctions grows and as the number of bidders increases.
- F. Beltrán, N. Santamaría, C. Restrepo, and P. Cardozo, “El teorema de ingreso equivalente para subastas de un objeto: Aproximación experimental,” Revista de Ingeniería, Universidad de Los Andes. Marzo, vol. 17, pp. 12–18, 2003.
- R. Gibbons, Game Theory for Applied Economists, Princeton University Press, New Jersey, 1992.
- P. Klemperer, Auctions: Theory and Practice, Princeton University Press, New Jersey, 2004.
- P. Milgrom, Putting Auction Theory to Work, Cambridge University Press, Cambridge, 2004.
- R. B. Myerson, “Optimal auction design,” Mathematics of Operations Research, vol. 6, no. 1, pp. 58–73, 1981.
- J. G. Riley and W. F. Samuelson, “Optimal auctions,” American Economic Review, vol. 71, pp. 381–392, 1981.
- K. Waehrer, R. M. Harstad, and M. H. Rothkopf, “Auction form preferences of risk-averse bid takers,” RAND Journal of Economics, vol. 29, no. 1, pp. 179–192, 1998.
Copyright © 2006 Fernando Beltrán and Natalia Santamaría. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.