skip to main content
10.1145/2600057.2602857acmconferencesArticle/Chapter ViewAbstractPublication PagesecConference Proceedingsconference-collections
abstract

Knightian self uncertainty in the vcg mechanism for unrestricted combinatorial auctions

Published:01 June 2014Publication History

ABSTRACT

We study the social welfare performance of the VCG mechanism in the well-known and challenging model of self uncertainty initially put forward by Frank H. Knight and later formalized by Truman F. Bewley. Namely, the only information that each player i has about his own true valuation consists of a set of distributions, from one of which i's valuation has been drawn.

We assume that each player knows his true valuation up to an additive inaccuracy δ, and study the social welfare performance of the VCG mechanism relative to δ > 0. Denoting by MSW the maximum social welfare, we have already shown in [Chiesa, Micali and Zhu 2012] that, even in single-good auctions, no mechanism can guarantee any social welfare greater than MSW / n in dominant strategies or ex-post Nash equilibrium strategies, where n is the number of players.

In a separate paper [CMZ14], we have proved that for multi-unit auctions, where it coincides with the Vickrey mechanism, the VCG mechanism performs very well in (Knightian) undominated strategies. Namely, in an n-player m-unit auction, the Vickrey mechanism guarantees a social welfare ≥ - MSW - 2mδ, when each Knightian player chooses an arbitrary undominated strategy to bid in the auction.

In this paper we focus on the social welfare performance of the VCG mechanism in unrestricted combinatorial auctions, both in undominated strategies and regret-minimizing strategies. (Indeed, both solution concepts naturally extend to the Knightian setting with player self uncertainty.)

Our first theorem proves that, in an n-player m-good combinatorial auction, the VCG mechanism may produce outcomes whose social welfare is ≤ - MSW - ω(2m δ), even when n=2 and each player chooses an undominated strategy. We also geometrically characterize the set of undominated strategies in this setting.

Our second theorem shows that the VCG mechanism performs well in regret-minimizing strategies: the guaranteed social welfare is ≥-MSW - 2min{m,n}δ if each player chooses a pure regret-minimizing strategy, and ≥- MSW - O(n2 δ) if mixed strategies are allowed.

Finally, we prove a lemma bridging two standard models of rationality: utility maximization and regret minimization. A special case of our lemma implies that, in any game (Knightian or not), every implementation for regret-minimizing players also applies to utility-maximizing players who use regret ONLY to break ties among their undominated strategies. This bridging lemma thus implies that the VCG mechanism continues to perform very well also for the latter players.

References

  1. Alessandro Chiesa, Silvio Micali, and Zeyuan Allen Zhu. 2012. Mechanism Design With Approximate Valuations. In Proceedings of the 3rd Innovations in Theoretical Computer Science conference (ITCS '12). Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Alessandro Chiesa, Silvio Micali, and Zeyuan Allen Zhu. 2014. Knightian Robustness of the Vickrey Mechanism. ArXiv e-prints abs/1403.6413 (March 2014). http://arxiv.org/abs/1403.6413.Google ScholarGoogle Scholar

Index Terms

  1. Knightian self uncertainty in the vcg mechanism for unrestricted combinatorial auctions

      Recommendations

      Comments

      Login options

      Check if you have access through your login credentials or your institution to get full access on this article.

      Sign in
      • Published in

        cover image ACM Conferences
        EC '14: Proceedings of the fifteenth ACM conference on Economics and computation
        June 2014
        1028 pages
        ISBN:9781450325653
        DOI:10.1145/2600057

        Copyright © 2014 Owner/Author

        Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

        Publisher

        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 1 June 2014

        Check for updates

        Qualifiers

        • abstract

        Acceptance Rates

        EC '14 Paper Acceptance Rate80of290submissions,28%Overall Acceptance Rate664of2,389submissions,28%

        Upcoming Conference

        EC '24
        The 25th ACM Conference on Economics and Computation
        July 8 - 11, 2024
        New Haven , CT , USA

      PDF Format

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader