## Abstract

We consider a game theoretic knapsack problem that has application to auctions for selling advertisements on Internet search engines. Consider n agents each wishing to place an object in the knapsack. Each agent has a private valuation for having their object in the knapsack and each object has a publicly known size. For this setting, we consider the design of auctions in which agents have an incentive to truthfully reveal their private valuations. Following the framework of Goldberg et al. [10], we look to design an auction that obtains a constant fraction of the profit obtainable by a natural optimal pricing algorithm that knows the agents' valuations and object sizes. We give an auction that obtains a constant factor approximation in the non-trivial special case where the knapsack has unlimited capacity. We then reduce the limited capacity version of the problem to the unlimited capacity version via an approximately efficient auction (i.e., one that maximizes the social welfare). This reduction follows from generalizable principles.

Original language | English (US) |
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Title of host publication | Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms |

Pages | 1083-1092 |

Number of pages | 10 |

DOIs | |

State | Published - Feb 28 2006 |

Event | Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms - Miami, FL, United States Duration: Jan 22 2006 → Jan 24 2006 |

### Other

Other | Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms |
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Country | United States |

City | Miami, FL |

Period | 1/22/06 → 1/24/06 |

## ASJC Scopus subject areas

- Software
- Mathematics(all)