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A Robustly Efficient Auction

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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".

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Bibliographic Info

Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 248.

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Length: 37 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:cca:wpaper:248

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Related research

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

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References

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  1. Zvika Neeman, 1998. "The Relevance of Private Information in Mechanism Design," Papers 0093, Boston University - Industry Studies Programme.
  2. Dirk Bergemann & Stephen Morris, 2008. "Robust Implementation in General Mechanisms," Cowles Foundation Discussion Papers 1666R, Cowles Foundation for Research in Economics, Yale University, revised Jan 2010.
  3. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Cowles Foundation Discussion Papers 1421, Cowles Foundation for Research in Economics, Yale University.
  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. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521551847.
  6. Dirk Bergemann & Stephen Morris, 2009. "Robust Implementation in Direct Mechanisms," Review of Economic Studies, Oxford University Press, vol. 76(4), pages 1175-1204.
  7. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust virtual implementation with incomplete information: Towards a reinterpretation of the Wilson doctrine," Working Papers 2007-14, Instituto MadrileƱo de Estudios Avanzados (IMDEA) Ciencias Sociales.
  8. McAfee, R Preston & McMillan, John & Reny, Philip J, 1989. "Extracting the Surplus in the Common-Value Auction," Econometrica, Econometric Society, vol. 57(6), pages 1451-59, November.
  9. Antonio Penta, 2012. "Higher Order Uncertainty and Information: Static and Dynamic Games," Econometrica, Econometric Society, vol. 80(2), pages 631-660, 03.
  10. Dirk Bergemann & Stephen Morris, 2007. "Robust Virtual Implementation," Cowles Foundation Discussion Papers 1609RR, Cowles Foundation for Research in Economics, Yale University, revised Jan 2009.
  11. repec:wop:humbsf:2000-72 is not listed on IDEAS
  12. 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, 03.
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