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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. 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.
  2. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1391-1402, November.
  3. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2010. "Rationalizable Implementation," Levine's Working Paper Archive 661465000000000022, David K. Levine.
  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. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, Econometric Society, vol. 2(1), pages 15-40, March.
  6. Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Working Papers 2002-11, Brown University, Department of Economics.
  7. Bergemann, Dirk & Morris, Stephen, 2011. "Robust implementation in general mechanisms," Games and Economic Behavior, Elsevier, Elsevier, vol. 71(2), pages 261-281, March.
  8. Dirk Bergemann & Stephen Morris, 2007. "Robust Virtual Implementation," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1609RR, Cowles Foundation for Research in Economics, Yale University, revised Jan 2009.
  9. Gale, David, 1989. "The Theory of Linear Economic Models," University of Chicago Press Economics Books, University of Chicago Press, edition 1, number 9780226278841, June.
  10. Benoît, Jean-Pierre & Ok, Efe A., 2008. "Nash implementation without no-veto power," Games and Economic Behavior, Elsevier, Elsevier, vol. 64(1), pages 51-67, September.
  11. P. Battigalli & M. Siniscalchi, 2002. "Rationalization and Incomplete Information," Princeton Economic Theory Working Papers, David K. Levine 9817a118e65062903de7c3577, David K. Levine.
  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, 2009. "Robust Implementation in Direct Mechanisms," Levine's Working Paper Archive 814577000000000109, David K. Levine.
  14. Dirk Bergemann & Stephen Morris, 2005. "Ex Post Implementation," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1502, Cowles Foundation for Research in Economics, Yale University.
  15. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer, Springer, vol. 28(1), pages 111-125, January.
  16. 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.
  17. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, Econometric Society, vol. 65(5), pages 1175-1200, September.
  18. Lipman Barton L., 1994. "A Note on the Implications of Common Knowledge of Rationality," Games and Economic Behavior, Elsevier, Elsevier, vol. 6(1), pages 114-129, January.
  19. 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.
  20. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, Elsevier, vol. 39(1), pages 14-33, June.
  21. 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.
  22. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 461-77, March.
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Citations

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Cited by:
  1. Dirk Bergemann & Stephen Morris, 2008. "Robust Implementation in General Mechanisms," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1666, Cowles Foundation for Research in Economics, Yale University.
  2. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2010. "Rationalizable Implementation," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1697R, Cowles Foundation for Research in Economics, Yale University.
  3. Artemov, Georgy & Kunimoto, Takashi & Serrano, Roberto, 2013. "Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine," Journal of Economic Theory, Elsevier, Elsevier, vol. 148(2), pages 424-447.
  4. Kyungmin Kim & Antonio Penta, 2012. "A Robustly Efficient Auction," Carlo Alberto Notebooks, Collegio Carlo Alberto 248, Collegio Carlo Alberto.
  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, American Economic Association, vol. 102(3), pages 325-29, May.

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