Theory of Computing Systems

, Volume 57, Issue 3, pp 549–575

Uniform Price Auctions: Equilibria and Efficiency


DOI: 10.1007/s00224-014-9537-9

Cite this article as:
Markakis, E. & Telelis, O. Theory Comput Syst (2015) 57: 549. doi:10.1007/s00224-014-9537-9


We study the Uniform Price Auction, one of the standard sealed-bid multi-unit auction formats in Auction Theory, for selling multiple identical units of a single good to multi-demand bidders. Contrary to the truthful and efficient multi-unit Vickrey auction, the Uniform Price Auction encourages strategic bidding and is generally inefficient, due to a “Demand Reduction” effect; bidders tend to bid for fewer (identical) units, so as to receive them at a lower uniform price. All the same, the uniform pricing rule is popular by its appeal to the anticipation that identical items should be identically priced. Its applications include, among others, sales of U.S. Treasury notes to investors and trade exchanges over the Internet facilitated by popular online brokers. In this work, we characterize pure undominated bidding strategies and give an algorithm for computing pure Nash equilibria in such strategies. Subsequently we show that their Price of Anarchy is \(\frac {e}{e-1}\). Finally, we show that the Price of Anarchy of mixed Bayes-Nash equilibria with undominated support is at most \(4-\frac {2}{k}\), where k is the number of auctioned items. To the best of our knowledge, our work provides the first (constructive) proof of existence of pure Nash equilibria in undominated strategies and the first performance evaluation (with respect to economic efficiency) of this popular auction format.


Uniform price auctionPrice of anarchySubmodular valuation functionsBayes-Nash equilibrium

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of InformaticsAthens University of Economics and BusinessAthensGreece