### Abstract

The Competition Complexity of an auction setting refers to the number of additional bidders necessary in order for the (deterministic, prior-independent, dominant strategy truthful) Vickrey-Clarke-Groves mechanism to achieve greater revenue than the (randomized, prior-dependent, Bayesian-truthful) optimal mechanism without the additional bidders. We prove that the competition complexity of bidders with additive valuations over independent items is at most (ln(1 + /) + 2), and also at most 9 . When ≤ , the first bound is optimal up to constant factors, even when the items are i.i.d. and regular. When ≥ , the second bound is optimal for the benchmark introduced by Eden et al.up to constant factors, even when the items are i.i.d. and regular. We further show that, while the Eden et al. benchmark is not necessarily tight in the ≥ regime, the competition complexity of bidders with additive valuations over even 2 i.i.d. regular items is indeed (1). Our main technical contribution is a reduction from analyzing the Eden et al. benchmark to proving stochastic dominance of certain random variables.

Original language | English (US) |
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Title of host publication | STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing |

Editors | Moses Charikar, Edith Cohen |

Publisher | Association for Computing Machinery |

Pages | 686-696 |

Number of pages | 11 |

ISBN (Electronic) | 9781450367059 |

DOIs | |

State | Published - Jun 23 2019 |

Event | 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 - Phoenix, United States Duration: Jun 23 2019 → Jun 26 2019 |

### Publication series

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

### Conference

Conference | 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 |
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Country | United States |

City | Phoenix |

Period | 6/23/19 → 6/26/19 |

### All Science Journal Classification (ASJC) codes

- Software

### Keywords

- Auctions
- Duality
- Multi-dimensional mechanism design
- Stochastic dominance

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## Cite this

*STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing*(pp. 686-696). (Proceedings of the Annual ACM Symposium on Theory of Computing). Association for Computing Machinery. https://doi.org/10.1145/3313276.3316405