### Abstract

We design algorithms for computing approximately revenue-maximizing sequential posted-pricing mechanisms (SPM) in K-unit auctions, in a standard Bayesian model. A seller has K copies of an item to sell, and there are n buyers, each interested in only one copy, and has some value for the item. The seller posts a price for each buyer, using Bayesian information about buyers' valuations, who arrive in a sequence. An SPM specifies the ordering of buyers and the posted prices, and may be adaptive or non-adaptive in its behavior. The goal is to design SPM in polynomial time to maximize expected revenue. We compare against the expected revenue of optimal SPM, and provide a polynomial time approximation scheme (PTAS) for both non-adaptive and adaptive SPMs. This is achieved by two algorithms: an efficient algorithm that gives a -approximation (and hence a PTAS for sufficiently large K), and another that is a PTAS for constant K. The first algorithm yields a non-adaptive SPM that yields its approximation guarantees against an optimal adaptive SPM - this implies that the adaptivity gap in SPMs vanishes as K becomes larger.

Original language | English (US) |
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Title of host publication | Internet and Network Economics - 6th International Workshop, WINE 2010, Proceedings |

Pages | 158-169 |

Number of pages | 12 |

DOIs | |

State | Published - Dec 1 2010 |

Event | 6th International Workshop on Internet and Network Economics, WINE 2010 - Stanford, CA, United States Duration: Dec 13 2010 → Dec 17 2010 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6484 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 6th International Workshop on Internet and Network Economics, WINE 2010 |
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Country | United States |

City | Stanford, CA |

Period | 12/13/10 → 12/17/10 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Internet and Network Economics - 6th International Workshop, WINE 2010, Proceedings*(pp. 158-169). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6484 LNCS). https://doi.org/10.1007/978-3-642-17572-5_13