On Random Sampling Auctions for Digital Goods

TL;DR

This paper proves that a specific random sampling auction for digital goods is 4-competitive in many cases, narrowing the gap between known bounds and the conjectured optimal ratio using probabilistic and dynamic programming methods.

Contribution

It establishes a 4-competitive bound for a broad class of instances and refines the competitive ratio for remaining cases, improving prior analysis.

Findings

Proves 4-competitiveness for large classes of instances

Shows a 4.68-competitive ratio for remaining instances

Uses probabilistic techniques and dynamic programming for bounds

Abstract

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.