## Abstract

A traditionally desired goal when designing auction mechanisms is incentive compatibility, i.e., ensuring that bidders fare best by truthfully reporting their preferences. A complementary goal, which has, thus far, received significantly less attention, is to preserve privacy, i.e., to ensure that bidders reveal no more information than necessary. We further investigate and generalize the approximate privacy model for two-party communication recently introduced by Feigenbaum et al. [8]. We explore the privacy properties of a natural class of communication protocols that we refer to as "dissection protocols". Dissection protocols include, among others, the bisection auction in [9,10] and the bisection protocol for the millionaires problem in [8]. Informally, in a dissection protocol the communicating parties are restricted to answering simple questions of the form "Is your input between the values α and β (under a pre-defined order over the possible inputs)?". We prove that for a large class of functions called tiling functions, which include the 2^{nd}-price Vickrey auction, there always exists a dissection protocol that provides a constant average-case privacy approximation ratio for uniform or "almost uniform" probability distributions over inputs. To establish this result we present an interesting connection between the approximate privacy framework and basic concepts in computational geometry. We show that such a good privacy approximation ratio for tiling functions does not, in general, exist in the worst case. We also discuss extensions of the basic setup to more than two parties and to non-tiling functions, and provide calculations of privacy approximation ratios for two functions of interest.

Original language | American English |
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Title of host publication | Algorithmic Game Theory - 4th International Symposium, SAGT 2011, Proceedings |

Pages | 44-56 |

Number of pages | 13 |

DOIs | |

State | Published - 2011 |

Externally published | Yes |

Event | 4th International Symposium on Algorithmic Game Theory, SAGT 2011 - Amalfi, Italy Duration: 17 Oct 2011 → 19 Oct 2011 |

### 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 | 6982 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 4th International Symposium on Algorithmic Game Theory, SAGT 2011 |
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Country/Territory | Italy |

City | Amalfi |

Period | 17/10/11 → 19/10/11 |

## Keywords

- Approximate Privacy
- Auctions
- Communication Protocols