Multiple unit auctions of an indivisible good

Abstract

This paper studies the properties of several multiple unit auctions in the context of a general model that allows for private values and common values as special cases. The benchmark for the analysis is provided by the characterization of optimal selling procedures for a seller that has several units of a homogeneous indivisible good to be sold extending the analysis of a single unit model in [1]. It is shown that the seller should impose endogenous individual minimum announcements, that are contingent on the bidders' reports and decreasing as the number of units allocated to the buyer increase. Implementation mechanisms are 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 mechanism, but some do not. Moreover, it is proven that in a sequential optimal auction the sequence of prices paid in each auction is a supermartingale, which conforms to the empirical behavior of prices in sequential auctions.