Abstract

We develop a general duality-theory framework for revenue maximization in additive Bayesian auctions. The framework extends linear programming duality and complementarity to constraints with partial derivatives. The dual system reveals the geometric nature of the problem and highlights its connection with the theory of bipartite graph matchings. We demonstrate the power of the framework by applying it to a multiple-good monopoly setting where the buyer has uniformly distributed valuations for the items, the canonical long-standing open problem in the area. We propose a deterministic selling mechanism called straight-jacket auction (SJA), which we prove to be exactly optimal for up to six items, and conjecture its optimality for any number of goods. The duality framework is used not only for proving optimality, but perhaps more importantly for deriving the optimal mechanism itself; as a result, SJA is defined by natural geometric constraints.

Keywords

  1. optimal auctions
  2. revenue maximization
  3. duality
  4. mechanism design

MSC codes

  1. 91A99
  2. 91B99

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Information & Authors

Information

Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 121 - 165
ISSN (online): 1095-7111

History

Submitted: 25 April 2016
Accepted: 31 July 2017
Published online: 24 January 2018

Keywords

  1. optimal auctions
  2. revenue maximization
  3. duality
  4. mechanism design

MSC codes

  1. 91A99
  2. 91B99

Authors

Affiliations

Yiannis Giannakopoulos

Funding Information

H2020 European Research Council https://doi.org/10.13039/100010663 : FP7/2007-2013, 321171

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