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A Robustly Efficient Auction

Author

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  • Kyungmin Kim
  • Antonio Penta

Abstract

We study the problem of efficient auction design in environments with interdependent values, under arbitrary common knowledge assumptions. We propose a simple mechanism and show that, under a rather mild condition, it "robustly" achieves efficiency. Our mechanism consists in a standard Vickrey auction, preceded by one round of communication, where agents report their private signals and receive transfers from the designer. We interpret the transfers as the cost for the designer to robustly achieve efficiency. We introduce a notion of robust informational size and show that the transfers are small if agents are informationally small in our sense. Furthermore, the transfers are decreasing in the amount of information available to the designer and in the strength of the common knowledge assumptions. In other words, the more robust the efficient implementation result, the higher the cost of achieving efficiency. We thus formalize the intuitive idea of a trade-off between robustness and efficient implementation and analyze the determinants of the "cost of robustness".

Suggested Citation

  • Kyungmin Kim & Antonio Penta, 2012. "A Robustly Efficient Auction," Carlo Alberto Notebooks 248, Collegio Carlo Alberto.
  • Handle: RePEc:cca:wpaper:248
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    File URL: http://www.carloalberto.org/assets/working-papers/no.248.pdf
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    References listed on IDEAS

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    1. Neeman, Zvika, 2004. "The relevance of private information in mechanism design," Journal of Economic Theory, Elsevier, vol. 117(1), pages 55-77, July.
    2. Bergemann, Dirk & Morris, Stephen, 2011. "Robust implementation in general mechanisms," Games and Economic Behavior, Elsevier, vol. 71(2), pages 261-281, March.
    3. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, April.
    4. Philippe Aghion & Drew Fudenberg & Richard Holden & Takashi Kunimoto & Olivier Tercieux, 2012. "Subgame-Perfect Implementation Under Information Perturbations," The Quarterly Journal of Economics, Oxford University Press, vol. 127(4), pages 1843-1881.
    5. Dirk Bergemann & Stephen Morris, 2005. "Robust Mechanism Design," Econometrica, Econometric Society, vol. 73(6), pages 1771-1813, November.
    6. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust Virtual Implementation with Incomplete Information: Toward a Reinterpretation of the Wilson Doctrine," Working Papers 2007-6, Brown University, Department of Economics.
    7. Antonio Penta, 2012. "Higher Order Uncertainty and Information: Static and Dynamic Games," Econometrica, Econometric Society, vol. 80(2), pages 631-660, March.
    8. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, vol. 75(2), pages 365-400, March.
    9. Bergemann, Dirk & Morris, Stephen, 2009. "Robust virtual implementation," Theoretical Economics, Econometric Society, vol. 4(1), March.
    10. McAfee, R Preston & McMillan, John & Reny, Philip J, 1989. "Extracting the Surplus in the Common-Value Auction," Econometrica, Econometric Society, vol. 57(6), pages 1451-1459, November.
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    More about this item

    Keywords

    Cost of robustness; efficient auctions; informational size; interdependent values; robust mechanism design;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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