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Robust Implementation: The Case of Direct Mechanisms"

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Abstract

A social choice function is robustly implementable if there is a mechanism under which the process of iteratively eliminating strictly dominated messages leads to outcomes that agree with the social choice at every type profile. In an interdependent value environment with single crossing preferences, we identify a strict contraction property on the preferences which together with strict ex post incentive compatibility is sufficient to guarantee robust implementation in the direct mechanism. Strict EPIC and the contraction property are also necessary for robust implementation in any mechanism. The contraction property essentially requires that the interdependence is not too large. In a linear signal model, the contraction property is equivalent to an interdependence matrix having an eigenvalue less than one.

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File URL: http://cowles.econ.yale.edu/P/cd/d15b/d1561-r.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1561R.

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Length: 39 pages
Date of creation: May 2006
Date of revision: May 2007
Publication status: Published in Review of Economic Studies (2009), 76: 1175-1204
Handle: RePEc:cwl:cwldpp:1561r

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Mechanism design; Implementation; Robustness; Common knowledge; Interim equilibrium; Iterative deletion; Direct mechanism;

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References

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  1. Partha Dasgupta & Eric Maskin, 2000. "Efficient Auctions," The Quarterly Journal of Economics, MIT Press, vol. 115(2), pages 341-388, May.
  2. Hong, Han & Shum, Matthew, 2003. "Econometric models of asymmetric ascending auctions," Journal of Econometrics, Elsevier, vol. 112(2), pages 327-358, February.
  3. Bergemann, Dirk & Morris, Stephen, 2008. "Ex post implementation," Games and Economic Behavior, Elsevier, vol. 63(2), pages 527-566, July.
  4. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
  5. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  6. P. Battigalli & M. Siniscalchi, 2002. "Rationalization and Incomplete Information," Princeton Economic Theory Working Papers 9817a118e65062903de7c3577, David K. Levine.
  7. Dirk Bergemann & Juuso Vaimaki, 2000. "Information Acquisition and Efficient Mechanism Design," Cowles Foundation Discussion Papers 1248, Cowles Foundation for Research in Economics, Yale University.
  8. Sushil Bikhchandani, 2004. "The Limits of Ex Post Implementation Revisited," Levine's Bibliography 122247000000000514, UCLA Department of Economics.
  9. Krishna, Vijay, 2003. "Asymmetric English auctions," Journal of Economic Theory, Elsevier, vol. 112(2), pages 261-288, October.
  10. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2005. "The Limits of Ex-Post Implementation," Levine's Bibliography 666156000000000548, UCLA Department of Economics.
  11. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  12. Kim-Sau Chung & Jeffrey C. Ely, 2000. "Efficient and Dominance Solvable Auctions with Interdependent Valuations," Discussion Papers 1313, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  13. repec:wop:humbsf:2000-72 is not listed on IDEAS
  14. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  15. Birulin, Oleksii & Izmalkov, Sergei, 2011. "On efficiency of the English auction," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1398-1417, July.
  16. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
  17. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Mechanism Design with Incomplete Information: A Solution to the Implementation Problem," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 668-91, June.
  18. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-61, March.
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Cited by:
  1. Dirk Bergemann & Stephen Morris, 2007. "An Ascending Auction for Independent Values: Uniqueness and Robustness to Strategic Uncertainty," Cowles Foundation Discussion Papers 1600, Cowles Foundation for Research in Economics, Yale University, revised Mar 2007.
  2. Stephen Morris & Dirk Bergemann, 2007. "An Ascending Auction for Interdependent Values: Uniqueness and Robustness to Strategic Uncertainty," American Economic Review, American Economic Association, vol. 97(2), pages 125-130, May.
  3. Dirk Bergemann & Stephen Morris, 2006. "Ex Post Implementation," Levine's Bibliography 122247000000001110, UCLA Department of Economics.
  4. Dirk Bergemann & Stephen Morris, 2007. "Dynamic Auctions: Uniqueness and Robustness to Private Information," Levine's Bibliography 321307000000000771, UCLA Department of Economics.
  5. Dirk Bergemann & Stephen Morris, 2007. "Ascending Auction: Uniqueness and Robustness to Strategic Uncertainty," Levine's Bibliography 321307000000000845, UCLA Department of Economics.

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