Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 27417, 14 pages

A measure of the variability of revenue in auctions: A look at the revenue equivalence theorem

Fernando Beltrán1 and Natalia Santamaría2,3

1Information Systems and Operations Management Department, University of Auckland Business School, Auckland 1142, New Zealand
2Departamento de Ingeniería Industrial, Universidad de los Andes, P.O. Box 4976, Bogotá, Colombia
3Rutgers Center for Operations Research (RUTCOR), Rutgers University, Piscataway 08854-8003, NJ, USA

Received 30 August 2005; Revised 6 June 2006; Accepted 7 June 2006

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.


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.