MULTIPLE-UNIT AUCTIONS OF AN INDIVISIBLE GOOD

This paper studies the properties of several multiple unit auctions in the context of a general model that allows for private values and com mon values as special cases. The benchmark for the analysis is provide d by the characterization of optimal selling procedures for a seller t hat has several units of a homogeneous indivisible good to be sold ext ending the analysis of a single unit model in [1]. It is shown that th e seller should impose endogenous individual minimum announcements, th at are contingent on the bidders' reports and decreasing as the number of units allocated to the buyer increase. Implementation mechanisms a re discussed in the context of a special case of the model. Under the assumption of unit demands, it is shown that some generalizations (to multiple units) of standard auctions may implement the optimal mechani sm, but some do not. Moreover, it is proven that in a sequential optim al auction the sequence of prices paid in each auction is a supermarti ngale, which conforms to the empirical behavior of prices in sequentia l auctions.