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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 122247000000002286.

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Date of creation: 28 Jul 2008
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Handle: RePEc:cla:levarc:122247000000002286

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References

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  1. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Levine's Bibliography 666156000000000035, UCLA Department of Economics.
  2. 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.
  3. Morris, Stephen & Dekel, Eddie & Fudenberg, Drew, 2007. "Interim Correlated Rationalizability," Scholarly Articles 3196333, Harvard University Department of Economics.
  4. Matthew 0. Jackson, 1989. "Implementation in Undominated Strategies - A Look at Bounded Mechanisms," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 833, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Dirk Bergemann & Stephen Morris, 2005. "Ex Post Implementation," Levine's Bibliography 784828000000000018, UCLA Department of Economics.
  6. Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Working Papers 2002-11, Brown University, Department of Economics.
  7. 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.
  8. Bergemann, Dirk & Morris, Stephen, 2011. "Robust implementation in general mechanisms," Games and Economic Behavior, Elsevier, Elsevier, vol. 71(2), pages 261-281, March.
  9. Gale, David, 1989. "The Theory of Linear Economic Models," University of Chicago Press Economics Books, University of Chicago Press, edition 1, number 9780226278841.
  10. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, Elsevier, vol. 39(1), pages 14-33, June.
  11. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, Econometric Society, vol. 65(5), pages 1175-1200, September.
  12. Bergemann, Dirk & Stephen Morris, 2006. "Robust Implementation in Direct Mechanisms," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1561RR, Cowles Foundation for Research in Economics, Yale University, revised Jan 2009.
  13. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 461-77, March.
  14. Bergemann, Dirk & Morris, Stephen & Tercieux, Olivier, 2011. "Rationalizable implementation," Journal of Economic Theory, Elsevier, Elsevier, vol. 146(3), pages 1253-1274, May.
  15. Dirk Bergemann & Stephen Morris, 2009. "Robust Virtual Implementation," Levine's Working Paper Archive 814577000000000155, David K. Levine.
  16. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1391-1402, November.
  17. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, De Gruyter, vol. 3(1), pages 1-46, June.
  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. 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.
  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. 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.
  22. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer, Springer, vol. 28(1), pages 111-125, January.
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Citations

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Cited by:
  1. Dirk Bergemann & Stephen Morris, 2008. "Robust Implementation in General Mechanisms," Levine's Working Paper Archive 122247000000002286, David K. Levine.
  2. Kyungmin Kim & Antonio Penta, 2012. "A Robustly Efficient Auction," Carlo Alberto Notebooks, Collegio Carlo Alberto 248, Collegio Carlo Alberto.
  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. Ghossoub, Mario, 2010. "Belief heterogeneity in the Arrow-Borch-Raviv insurance model," MPRA Paper 37630, University Library of Munich, Germany, revised 22 Mar 2012.
  5. 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.
  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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