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From Optimal Limited to Unlimited Supply Auctions

By Jason D. Hartline

Abstract

We investigate the class of single-round, sealed-bid auctions for a set of identical items to bidders who each desire one unit. We adopt the worst-case competitive framework defined by [9, 5] that compares the profit of an auction to that of an optimal single-price sale of least two items. In this paper, we first derive an optimal auction for three items, answering an open question from [8]. Second, we show that the form of this auction is independent of the competitive framework used. Third, 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 items, we achieve an auction with a competitive ratio of 3.25, which improves upon the previously best-known competitive ratio of 3.39 from [7]. Finally, we generalize a result from [8] 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

Topics: Sciences, Economics General Terms Algorithms, Economics, Theory Keywords Auctions, Mechanism Design, Competitive Analysis
Publisher: ACM Press
Year: 2005
OAI identifier: oai:CiteSeerX.psu:10.1.1.134.3409
Provided by: CiteSeerX
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