## Abstract

We consider a monopolist that is selling n items to a single additive buyer, where the buyer's values for the items are drawn according to independent distributions F_{1}, F_{2},⋯, F_{n} that possibly have unbounded support. It is well known that - unlike in the single item case - the revenue-optimal auction (a pricing scheme) may be complex, sometimes requiring a continuum of menu entries. It is also known that simple auctions with a finite bounded number of menu entries can extract a constant fraction of the optimal revenue. Nonetheless, the question of the possibility of extracting an arbitrarily high fraction of the optimal revenue via a finite menu size remained open. In this paper, we give an affirmative answer to this open question, showing that for every n and for every ϵ > 0, there exists a complexity bound C = C(n, ϵ) such that auctions of menu size at most C suffice for obtaining a (1 - ϵ) fraction of the optimal revenue from any F_{1},⋯, F_{n}. We prove upper and lower bounds on the revenue approximation complexity C(n, ϵ), as well as on the deterministic communication complexity required to run an auction that achieves such an approximation.

Original language | American English |
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Title of host publication | STOC 2017 - Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing |

Editors | Pierre McKenzie, Valerie King, Hamed Hatami |

Publisher | Association for Computing Machinery |

Pages | 869-877 |

Number of pages | 9 |

ISBN (Electronic) | 9781450345286 |

DOIs | |

State | Published - 19 Jun 2017 |

Event | 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017 - Montreal, Canada Duration: 19 Jun 2017 → 23 Jun 2017 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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Volume | Part F128415 |

ISSN (Print) | 0737-8017 |

### Conference

Conference | 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017 |
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Country/Territory | Canada |

City | Montreal |

Period | 19/06/17 → 23/06/17 |

### Bibliographical note

Publisher Copyright:© 2017 Copyright held by the owner/author(s).

## Keywords

- Approximate revenue maximization
- Auction
- Menu size
- Revenue maximization