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Beckmann's approach to multi-item multi-bidder auctions

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Listed:
  • Alexander V. Kolesnikov
  • Fedor Sandomirskiy
  • Aleh Tsyvinski
  • Alexander P. Zimin

Abstract

We consider the problem of revenue-maximizing Bayesian auction design with several bidders having independent private values over several items. We show that it can be reduced to the problem of continuous optimal transportation introduced by Beckmann (1952) where the optimal transportation flow generalizes the concept of ironed virtual valuations to the multi-item setting. We establish the strong duality between the two problems and the existence of solutions. The results rely on insights from majorization and optimal transportation theories and on the characterization of feasible interim mechanisms by Hart and Reny (2015).

Suggested Citation

  • Alexander V. Kolesnikov & Fedor Sandomirskiy & Aleh Tsyvinski & Alexander P. Zimin, 2022. "Beckmann's approach to multi-item multi-bidder auctions," Papers 2203.06837, arXiv.org, revised Sep 2022.
    • Handle: RePEc:arx:papers:2203.06837
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    References listed on IDEAS

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