Equilibria in a Multi-object Uniform Price Sealed Bid Auction with Multi-unit Demands

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.