In many existing markets demanders wish to buy more than one unit from a group of identical units of a commodity. Often, the units are sold simultaneously by auction. The vast majority of literature pertaining to the economics of auctions, however, considers environments in which demanders buy at most one object. In this paper we derive necessary and sufficient conditions for a set of bidding strategies to be a symmetric monotone Bayes-Nash equilibrium to a uniform price sealed bid auction using the
first rejected bid pricing rule
in an independent private values environment with two-unit demands. In any symmetric monotone Bayes-Nash equilibrium, all bidders submit one bid equal to their higher valuation and one bid lower than their lower valuation. We characterize the equilibrium and derive the exact amount of underrevelation in the lower bid.
This article is based on chapter 2 of the author's Ph.D. thesis. I would like to acknowledge the financial support of the Clarence Hicks Memorial Fellowship, the California Institute of Technology and the Jet Propulsion Laboratory. I also thank D. Roderick Kiewiet, Richard McKelvey, Charles Plott, David Porter, Annemieke Tromp, participants in the Tinbergen Institute Seminar Series, an anonymous referee and especially John Ledyard for countless enlightening comments.