Budget constrained auctions with heterogeneous items

Conference Paper

In this paper, we present the first approximation algorithms for the problem of designing revenue optimal Bayesian incentive compatible auctions when there are multiple (heterogeneous) items and when bidders have arbitrary demand and budget constraints (and additive valuations). Our mechanisms are surprisingly simple: We show that a sequential all-pay mechanism is a 4 approximation to the revenue of the optimal ex-interim truthful mechanism with a discrete type space for each bidder, where her valuations for different items can be correlated. We also show that a sequential posted price mechanism is a O(1) approximation to the revenue of the optimal ex-post truthful mechanism when the type space of each bidder is a product distribution that satisfies the standard hazard rate condition. We further show a logarithmic approximation when the hazard rate condition is removed, and complete the picture by showing that achieving a sub-logarithmic approximation, even for regular distributions and one bidder, requires pricing bundles of items. Our results are based on formulating novel LP relaxations for these problems, and developing generic rounding schemes from first principles. © 2010 ACM.

Full Text

Duke Authors

Cited Authors

  • Bhattacharya, S; Goel, G; Gollapudi, S; Munagala, K

Published Date

  • July 23, 2010

Published In

Start / End Page

  • 379 - 387

International Standard Serial Number (ISSN)

  • 0737-8017

International Standard Book Number 13 (ISBN-13)

  • 9781605588179

Digital Object Identifier (DOI)

  • 10.1145/1806689.1806743

Citation Source

  • Scopus