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Simple versus optimal mechanisms

Published: 06 July 2009 Publication History

Abstract

The monopolist's theory of optimal single-item auctions for agents with independent private values can be summarized by two statements. The first is from Myerson [8]: the optimal auction is Vickrey with a reserve price. The second is from Bulow and Klemperer [1]: it is better to recruit one more bidder and run the Vickrey auction than to run the optimal auction. These results hold for single-item auctions under the assumption that the agents' valuations are independently and identically drawn from a distribution that satisfies a natural (and prevalent) regularity condition.
These fundamental guarantees for the Vickrey auction fail to hold in general single-parameter agent mechanism design problems. We give precise (and weak) conditions under which approximate analogs of these two results hold, thereby demonstrating that simple mechanisms remain almost optimal in quite general single-parameter agent settings.

References

[1]
J. Bulow and P. Klemperer. Auctions versus negotiations. American Economic Review, 86(1):180--194, 1996.
[2]
S. Chawla, J.D. Hartline, and R.D. Kleinberg. Algorithmic pricing via virtual valuations. In Proc. 9th ACM Conf. on Electronic Commerce (EC), pages 243--251, 2007.
[3]
R. Day and P. Milgrom. Core-selecting auctions. International Journal of Game Theory, 36(3-4):393--407, 2008.
[4]
S. Dughmi, T. Roughgarden, and M. Sundararajan. Revenue submodularity. In these proceedings.
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A.V. Goldberg, J.D. Hartline, A. Karlin, M. Saks, and A. Wright. Competitive auctions. Games and Economic Behavior, 55(2):242--269, 2006.
[6]
J.D. Hartline and T. Roughgarden. Optimal mechanism design and money burning. In Proc. 39th ACM Symp. on Theory of Computing (STOC), pages 75--84, 2008.
[7]
A. Karlin, D. Kempe, and T. Tamir. Beyond VCG: Frugality in truthful mechanisms. In Proc. 46th IEEE Symp. on Foundations of Computer Science (FOCS), pages 615--626, 2005.
[8]
R. Myerson. Optimal auction design. Mathematics of Operations Research, 6(1):58--73, 1981.
[9]
Z. Neeman. The effectiveness of English auctions. Games and Economic Behavior, 43(2):214--238, 2003.
[10]
A. Ronen. On approximating optimal auctions. In Proc. 3rd ACM Conf. on Electronic Commerce (EC), pages 11--17, 2001.
[11]
A. Schrijver. Combinatorial Optimziation: Polyhedra and Efficiency. Springer, 2003.
[12]
K. Talwar. The price of truth: Frugality in truthful mechanisms. In Proc. 20th Annual Symp. on Theoretical Aspects of Computer Science (STACS), pages 608--619, 2003.

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    cover image ACM Conferences
    EC '09: Proceedings of the 10th ACM conference on Electronic commerce
    July 2009
    376 pages
    ISBN:9781605584584
    DOI:10.1145/1566374
    • General Chair:
    • John Chuang,
    • Program Chairs:
    • Lance Fortnow,
    • Pearl Pu
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    Published: 06 July 2009

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    Author Tags

    1. auctions
    2. optimal auctions
    3. revenue-maximization
    4. vcg mechanism
    5. vickrey auction

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    July 6 - 10, 2009
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