From optimal limited to unlimited supply auctions

Jason D. Hartline, Robert McGrew
2005 Proceedings of the 6th ACM conference on Electronic commerce - EC '05  
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,
more » ... e 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.
doi:10.1145/1064009.1064028 dblp:conf/sigecom/HartlineM05 fatcat:zg7uigoimjgjnezen4fndzmfpe