Auction Mechanism for Optimally Trading Off Revenue and Efficiency in Multi-unit Auctions

We study auctioning multiple units of the same good to potential buyers with single unit demand (i.e. every buyer wants only one unit of the good). Depending on the objective of the seller, different selling mechanisms are desirable. The Vickrey auction with a truthful reserve price is optimal when the objective is efficiency allocating the units to the parties who values them the most. The Myerson auction is optimal when the objective is the seller’s expected utility. These two objectives are generally in conflict, and cannot be maximized with one mechanism. In many realworld settings—such as privatization and competing electronic marketplaces—it is not clear that the objective should be either efficiency or seller’s expected utility. Typically, one of these objectives should weigh more than the other, but both are important. We account for both objectives by designing a new deterministic dominant strategy auction mechanism that maximizes expected social welfare subject to a minimum constraint on the seller’s expected utility. This way the seller can maximize social welfare subject to doing well enough for himself. The results in this paper are derived under the asymmetric independent private values model, which assumes that the distributions of buyers’ valuations are common knowledge. We also describe a prior-free mechanism, which does not assume that the distributions are known. When the number of buyers tends to infinity and the number of units on sale is at least two, this auction approaches expected efficiency and expected seller’s utility of the auction, designed with distributions known upfront.