{"title":"On Random Sampling Auctions for Digital Goods","authors":"S. Alaei, Azarakhsh Malekian, A. Srinivasan","doi":"10.1145/2517148","DOIUrl":null,"url":null,"abstract":"In the context of auctions for digital goods, an interesting random sampling auction has been proposed by Goldberg et al. [2001]. This auction has been analyzed by Feige et al. [2005], who have shown that it obtains in expectation at least 1/15 fraction of the optimal revenue, which is substantially better than the previously proven constant bounds but still far from the conjectured lower bound of 1/4. In this article, we prove that the aforementioned random sampling auction obtains at least 1/4 fraction of the optimal revenue for a large class of instances where the number of bids above (or equal to) the optimal sale price is at least 6. We also show that this auction obtains at least 1/4.68 fraction of the optimal revenue for the small class of remaining instances, thus leaving a negligible gap between the lower and upper bound. We employ a mix of probabilistic techniques and dynamic programming to compute these bounds.","PeriodicalId":194623,"journal":{"name":"ACM Trans. Economics and Comput.","volume":"188 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Trans. Economics and Comput.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2517148","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
In the context of auctions for digital goods, an interesting random sampling auction has been proposed by Goldberg et al. [2001]. This auction has been analyzed by Feige et al. [2005], who have shown that it obtains in expectation at least 1/15 fraction of the optimal revenue, which is substantially better than the previously proven constant bounds but still far from the conjectured lower bound of 1/4. In this article, we prove that the aforementioned random sampling auction obtains at least 1/4 fraction of the optimal revenue for a large class of instances where the number of bids above (or equal to) the optimal sale price is at least 6. We also show that this auction obtains at least 1/4.68 fraction of the optimal revenue for the small class of remaining instances, thus leaving a negligible gap between the lower and upper bound. We employ a mix of probabilistic techniques and dynamic programming to compute these bounds.