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Robust Implementation in General Mechanisms

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Abstract

A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation. Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces.

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File URL: http://cowles.econ.yale.edu/P/cd/d16b/d1666-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 1666R.

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Length: 41 pages
Date of creation: Jun 2008
Date of revision: Jan 2010
Publication status: Published in Games and Economic Behavior (2011), 71: 261-281
Handle: RePEc:cwl:cwldpp:1666r

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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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; Dominant strategies;

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References

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  1. Gale, David, 1989. "The Theory of Linear Economic Models," University of Chicago Press Economics Books, University of Chicago Press, edition 1, number 9780226278841, March.
  2. Dirk Bergemann & Stephen Morris, 2006. "Ex Post Implementation," Levine's Bibliography 122247000000001110, UCLA Department of Economics.
  3. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1391-1402, November.
  4. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1421R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2004.
  5. Benoît, Jean-Pierre & Ok, Efe A., 2008. "Nash implementation without no-veto power," Games and Economic Behavior, Elsevier, vol. 64(1), pages 51-67, September.
  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. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2006. "Interim Correlated Rationalizability," Levine's Bibliography 122247000000001188, UCLA Department of Economics.
  8. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, Econometric Society, vol. 60(5), pages 993-1008, September.
  9. BOCHET, Olivier, 2005. "Nash implementation with lottery mechanisms," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2005072, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February.
  11. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, Econometric Society, vol. 60(6), pages 1439-42, November.
  12. Jackson, Matthew O, 1992. "Implementation in Undominated.Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 59(4), pages 757-75, October.
  13. Dirk Bergemann & Stephen Morris, 2008. "Robust Implementation in General Mechanisms," Levine's Working Paper Archive 122247000000002286, David K. Levine.
  14. Dirk Bergemann & Stephen Morris, 2009. "Robust Virtual Implementation," Levine's Working Paper Archive 814577000000000155, David K. Levine.
  15. P. Battigalli & M. Siniscalchi, 2002. "Rationalization and Incomplete Information," Princeton Economic Theory Working Papers, David K. Levine 9817a118e65062903de7c3577, David K. Levine.
  16. Bergemann, Dirk & Morris, Stephen & Tercieux, Olivier, 2011. "Rationalizable implementation," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1253-1274, May.
  17. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 461-77, March.
  18. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
  19. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, Econometric Society, vol. 65(5), pages 1175-1200, September.
  20. Kim-Sau Chung & Jeffrey C. Ely, 2000. "Efficient and Dominance Solvable Auctions with Interdependent Valuations," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1313, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  21. Lipman Barton L., 1994. "A Note on the Implications of Common Knowledge of Rationality," Games and Economic Behavior, Elsevier, vol. 6(1), pages 114-129, January.
  22. 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, University of Chicago Press, vol. 97(3), pages 668-91, June.
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Citations

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Cited by:
  1. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2010. "Rationalizable Implementation," Levine's Working Paper Archive 661465000000000022, David K. Levine.
  2. Artemov, Georgy & Kunimoto, Takashi & Serrano, Roberto, 2013. "Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine," Journal of Economic Theory, Elsevier, vol. 148(2), pages 424-447.
  3. Kyungmin Kim & Antonio Penta, 2012. "A Robustly Efficient Auction," Carlo Alberto Notebooks, Collegio Carlo Alberto 248, Collegio Carlo Alberto.
  4. Dirk Bergemann & Stephen Morris, 2008. "Robust Implementation in General Mechanisms," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1666R, Cowles Foundation for Research in Economics, Yale University, revised Jan 2010.
  5. Ghossoub, Mario, 2010. "Belief heterogeneity in the Arrow-Borch-Raviv insurance model," MPRA Paper 37630, University Library of Munich, Germany, revised 22 Mar 2012.
  6. Tilman Borgers & Doug Smith, 2012. "Robustly Ranking Mechanisms," American Economic Review, American Economic Association, vol. 102(3), pages 325-29, May.

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