From optimal limited to unlimited supply auctions

We investigate the class of single-round, sealed-bid auctions for a set of identical items in unlimited supply. We adopt the worst-case competitive framework defined by [8, 4] that compares the profit of an auction to that of an optimal single-price sale to at least two bidders. In this paper, we first derive an optimal auction for three bidders, answering an open question from [7]. Second, we propose a schema for converting a given limited-supply auction into an unlimited supply auction. Applying this technique to our optimal auction for three bidders, we achieve an auction with a competitive ratio of 3.25, which improves upon the previously best-known competitive ratio of 3.39 from [6]. Finally, we generalize a result from [7] and extend our understanding of the nature of the optimal competitive auction by showing that the optimal competitive auction occasionally offers prices that are higher than all bid values.

• Type: Conference
• Year: 2005
• Where: SIGECOM
• Authors: Jason D. Hartline, Robert McGrew
• Keywords: Auction, Optimal Auction, Optimal Competitive Auction, SIGECOM 2005