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Valuation compressions in VCG-based combinatorial auctions

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  • Dütting, Paul
  • Henzinger, Monika
  • Starnberger, Martin

Abstract

The focus of classic mechanism design has been on truthful direct-revelation mechanisms. In the context of combinatorial auctions the truthful direct-revelation mechanism that maximizes social welfare is the VCG mechanism. For many valuation spaces computing the allocation and payments of the VCG mechanism, however, is a computationally hard problem. We thus study the performance of the VCG mechanism when bidders are forced to choose bids from a subspace of the valuation space for which the VCG outcome can be computed efficiently. We prove improved upper bounds on the welfare loss for restrictions to additive bids and upper and lower bounds for restrictions to non-additive bids. These bounds show that increased expressiveness can give rise to additional equilibria of poorer efficiency.

Suggested Citation

  • Dütting, Paul & Henzinger, Monika & Starnberger, Martin, 2018. "Valuation compressions in VCG-based combinatorial auctions," LSE Research Online Documents on Economics 87419, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:87419
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    File URL: http://eprints.lse.ac.uk/87419/
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    References listed on IDEAS

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    5. Milgrom, Paul, 2010. "Simplified mechanisms with an application to sponsored-search auctions," Games and Economic Behavior, Elsevier, vol. 70(1), pages 62-70, September.
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    Cited by:

    1. Paul Dütting & Felix Fischer & David C. Parkes, 2019. "Expressiveness and Robustness of First-Price Position Auctions," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 196-211, February.
    2. Feldman, Michal & Shabtai, Galia, 2023. "Simultaneous 2nd price item auctions with no-underbidding," Games and Economic Behavior, Elsevier, vol. 140(C), pages 316-340.
    3. Paul Dütting & Thomas Kesselheim & Éva Tardos, 2021. "Algorithms as Mechanisms: The Price of Anarchy of Relax and Round," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 317-335, February.

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    More about this item

    Keywords

    algorithms; economics; theory; simplified mechanisms; combinatorial auctions with item bidding; price of anarchy;
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    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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