### Abstract

We consider the problem of a single seller repeatedly selling a single item to a single buyer (specifically, the buyer has a value drawn fresh from known distribution D in every round). Prior work assumes that the buyer is fully rational and will perfectly reason about how their bids today affect the seller's decisions tomorrow. In this work we initiate a different direction: the buyer simply runs a no-regret learning algorithm over possible bids. We provide a fairly complete characterization of optimal auctions for the seller in this domain. Specifically: • If the buyer bids according to EXP3 (or any “mean-based” learning algorithm), then the seller can extract expected revenue arbitrarily close to the expected welfare. This auction is independent of the buyer's valuation D, but somewhat unnatural as it is sometimes in the buyer's interest to overbid. • There exists a learning algorithm A such that if the buyer bids according to A then the optimal strategy for the seller is simply to post the Myerson reserve for D every round. • If the buyer bids according to EXP3 (or any “mean-based” learning algorithm), but the seller is restricted to “natural” auction formats where overbidding is dominated (e.g. Generalized First-Price or Generalized Second-Price), then the optimal strategy for the seller is a pay-your-bid format with decreasing reserves over time. Moreover, the seller's optimal achievable revenue is characterized by a linear program, and can be unboundedly better than the best truthful auction yet simultaneously unboundedly worse than the expected welfare.

Original language | English (US) |
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Title of host publication | ACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation |

Publisher | Association for Computing Machinery, Inc |

Pages | 523-538 |

Number of pages | 16 |

ISBN (Electronic) | 9781450358293 |

DOIs | |

State | Published - Jun 11 2018 |

Event | 19th ACM Conference on Economics and Computation, EC 2018 - Ithaca, United States Duration: Jun 18 2018 → Jun 22 2018 |

### Publication series

Name | ACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation |
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### Other

Other | 19th ACM Conference on Economics and Computation, EC 2018 |
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Country | United States |

City | Ithaca |

Period | 6/18/18 → 6/22/18 |

### All Science Journal Classification (ASJC) codes

- Computer Science (miscellaneous)
- Statistics and Probability
- Computational Mathematics
- Economics and Econometrics

### Keywords

- Auctions
- Mechanism design
- Multi-armed bandits
- No-regret learning

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## Cite this

*ACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation*(pp. 523-538). (ACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation). Association for Computing Machinery, Inc. https://doi.org/10.1145/3219166.3219233