On Random Sampling Auctions for Digital Goods

In the context of auctions for digital goods, an interesting random sampling auction has been proposed by Goldberg, Hartline, and Wright [2001]. This auction has been analyzed by Feige, Flaxman, Hartline, and Kleinberg [2005], who have shown that it is 15-competitive in the worst case {which is substantially better than the previously proven constant bounds but still far from the conjectured competitive ratio of 4. In this paper, we prove that the aforementioned random sampling auction is indeed 4-competitive 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 it is 4:68-competitive 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.
Comment: A preliminary version appeared in the 10th ACM conference on Electronic Commerce, 2009