## Abstract

In the design and analysis of revenue-maximizing auctions, auction performance is typically measured with respect to a prior distribution over inputs. The most obvious source for such a distribution is past data. The goal of this paper is to understand how much data is necessary and sufficient to guarantee near-optimal expected revenue. Our basic model is a single-item auction in which bidders' valuations are drawn independently from unknown and nonidentical distributions. The seller is given m samples from each of these distributions "for free" and chooses an auction to run on a fresh sample. How large does m need to be, as a function of the number k of bidders and ε > 0, so that a (1 - ε)-approximation of the optimal revenue is achievable? We prove that, under standard tail conditions on the underlying distributions, m = poly(k, 1/ε) samples are necessary and sufficient. Our lower bound stands in contrast to many recent results on simple and prior-independent auctions and fundamentally involves the interplay between bidder competition, non-identical distributions, and a very close (but still constant) approximation of the optimal revenue. It effectively shows that the only way to achieve a sufficiently good constant approximation of the optimal revenue is through a detailed understanding of bidders' valuation distributions. Our upper bound is constructive and applies in particular to a variant of the empirical Myerson auction, the natural auction that runs the revenue-maximizing auction with respect to the empirical distributions of the samples. To capture how our sample complexity upper bound depends on the set of allowable distributions, we introduce α-strongly regular distributions, which interpolate between the well-studied classes of regular (α = 0) and MHR (α = 1) distributions. We give evidence that this definition is of independent interest.

Original language | English (US) |
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Title of host publication | STOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing |

Publisher | Association for Computing Machinery |

Pages | 243-252 |

Number of pages | 10 |

ISBN (Print) | 9781450327107 |

DOIs | |

State | Published - 2014 |

Event | 4th Annual ACM Symposium on Theory of Computing, STOC 2014 - New York, NY, United States Duration: May 31 2014 → Jun 3 2014 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN (Print) | 0737-8017 |

### Other

Other | 4th Annual ACM Symposium on Theory of Computing, STOC 2014 |
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Country | United States |

City | New York, NY |

Period | 5/31/14 → 6/3/14 |

## Keywords

- Myerson's auction
- Sample complexity

## ASJC Scopus subject areas

- Software