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Robust Implementation in General Mechanisms

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  • Dirk Bergemann
  • Stephen Morris

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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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 661465000000000017.

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Date of creation: 17 Mar 2010
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Handle: RePEc:cla:levarc:661465000000000017

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  1. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
  2. Gale, David, 1989. "The Theory of Linear Economic Models," University of Chicago Press Economics Books, University of Chicago Press, edition 1, number 9780226278841.
  3. Jackson, Matthew O, 1992. "Implementation in Undominated.Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 59(4), pages 757-75, October.
  4. Morris, Stephen & Dekel, Eddie & Fudenberg, Drew, 2007. "Interim Correlated Rationalizability," Scholarly Articles 3196333, Harvard University Department of Economics.
  5. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2010. "Rationalizable Implementation," Levine's Working Paper Archive 661465000000000022, David K. Levine.
  6. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Cowles Foundation Discussion Papers 1421R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2004.
  7. Dirk Bergemann & Stephen Morris, 2005. "Ex Post Implementation," Levine's Bibliography 784828000000000018, UCLA Department of Economics.
  8. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
  9. P. Battigalli & M. Siniscalchi, 2002. "Rationalization and Incomplete Information," Princeton Economic Theory Working Papers 9817a118e65062903de7c3577, David K. Levine.
  10. Bergemann, Dirk & Morris, Stephen, 2009. "Robust virtual implementation," Theoretical Economics, Econometric Society, vol. 4(1), March.
  11. BOCHET, Olivier, 2005. "Nash implementation with lottery mechanisms," CORE Discussion Papers 2005072, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. 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.
  13. Dirk Bergemann & Stephen Morris, 2009. "Robust Implementation in Direct Mechanisms," Review of Economic Studies, Oxford University Press, vol. 76(4), pages 1175-1204.
  14. 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.
  15. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  16. 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.
  17. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-42, November.
  18. 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.
  19. 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.
  20. Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Working Papers 2002-11, Brown University, Department of Economics.
  21. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  22. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
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Citations

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Cited by:
  1. Dirk Bergemann & Stephen Morris, 2009. "Rationalizable Implementation," Cowles Foundation Discussion Papers 1697, Cowles Foundation for Research in Economics, Yale University.
  2. Ghossoub, Mario, 2010. "Belief heterogeneity in the Arrow-Borch-Raviv insurance model," MPRA Paper 37630, University Library of Munich, Germany, revised 22 Mar 2012.
  3. Kyungmin Kim & Antonio Penta, 2012. "A Robustly Efficient Auction," Carlo Alberto Notebooks 248, Collegio Carlo Alberto.
  4. Tilman Borgers & Doug Smith, 2012. "Robustly Ranking Mechanisms," American Economic Review, American Economic Association, vol. 102(3), pages 325-29, May.
  5. Dirk Bergemann & Stephen Morris, 2008. "Robust Implementation in General Mechanisms," Levine's Working Paper Archive 122247000000002286, David K. Levine.
  6. 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.

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