An equilibrium analysis of the simultaneous ascending auction

We provide a Bayes-Nash equilibrium analysis of the simultaneous ascending auction (SAA) when local bidders interested in a single item compete against global bidders interested in aggregating many items. We first assume that each local bidder values only a specific item, e.g. the license for the region where it has monopoly power, and that global bidders’ valuation functions are convex. For this environment we show that a global bidder faces an exposure problem with adverse consequences for revenue and efficiency. In the limit when the number of items grows large, the SAA is revenue and efficiency equivalent to the Vickrey-Clarke-Groves (VCG) mechanism. We extend our analysis to include the case where items are substitutes for local bidders, so that price arbitrage will occur as observed in many spectrum auctions. This environment, which combines substitutes and complements, results in an aggravated exposure problem. Consequently, the SAA is no longer efficient and may yield dramatically lower revenues than the VCG mechanism. Finally, we relax the assumption that global bidders’ valuation functions are convex by considering an environment with medium-sized global bidders who demand fewer than all items. We show that global bidders divide the market at low prices when market sharing is feasible while they engage in mutually destructive bidding when there is a fitting problem. In both cases, the SAA again underperforms relative to the VCG mechanism. ∗Goeree: Chair for Organizational Design, University of Zürich, Blümlisalpstrasse 10, CH-8006, Zürich, Switzerland. Lien: Department of Economics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong. We gratefully acknowledge financial support from the European Research Council (ERC Advanced grant, ESEI-249433). We thank Oleg Baranov, Alexey Kushnir, participants at the “Rothkopf Memorial Conference” (Penn State, June 2009), the “International Game Theory Meetings” (Stony Brook, July 2009), the “Wilson Scholar Lecture” (University of Arizona, November 2009), and the “Industrial Organization: Theory, Empirics, and Experiments,” (Lecce, July 2011), as well as seminar participants at the University of Edinburgh (February 2010), Carlos III Madrid (March 2010), UCL (May 2010), Bocconi University (January, 2011), University of Munich (February 2011), Paris School of Economics (March, 2011), Collegio Alberto (April, 2011), University of Cologne (May, 2011), University of Basel (May, 2011), GREQAM Marseille (May, 2011), UPF Barcelona (October 2011) for helpful comments.