An optimal auction for capacity constrained bidders: a network perspective

Economic Theory volume 39, pages113–128(2009)Cite this article

Abstract

This paper examines the problem of a seller with limited supply selling to a group of agents whose private information is two-dimensional. Each agent has a constant marginal value for the good up to some capacity, thereafter it is zero. Both the marginal value and the capacity are private information. We describe the revenue maximizing Bayesian incentive compatible auction for this environment. A novel feature of the analysis is an interpretation of an optimal auction design problem in terms of a linear program that is an instance of a parametric shortest path problem on a lattice.

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Author information

Affiliations

  1. Sam M. Walton College of Business, University of Arkansas, Fayetteville, AR, 72701, USA

    Alexey Malakhov

  2. Kellogg School of Management, Northwestern University, Evanston, IL, 60208-2001, USA

    Rakesh V. Vohra

Authors
  1. Alexey Malakhov
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  2. Rakesh V. Vohra
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Corresponding author

Correspondence to Alexey Malakhov.

Additional information

We thank the referees for a number of useful suggestions that have been incorporated into the paper. Mallesh Pai suggested the argument given in Lemma 1. The research was supported in part by the NSF grant ITR IIS-0121678.

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Malakhov, A., Vohra, R.V. An optimal auction for capacity constrained bidders: a network perspective. Econ Theory 39, 113–128 (2009). https://doi.org/10.1007/s00199-007-0312-x

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Keywords

  • Auctions
  • Networks
  • Linear programming

JEL Classification

  • C61
  • C70
  • D44