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Robust Implementation: The Role of Large Type Spaces

A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with a social choice function. 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. It requires that there not be too much interdependence of types. We characterize robust monotonicity for some interesting economic environments. We identify conditions where, if robust implementation is possible, it is possible in a direct mechanism. We identify conditions where, if robust implementation is not possible, virtual robust implementation is not possible either.

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File URL: http://cowles.econ.yale.edu/P/cd/d15a/d1519.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1519.

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Length: 59 pages
Date of creation: Jun 2005
Date of revision:
Handle: RePEc:cwl:cwldpp:1519
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Web page: http://cowles.econ.yale.edu/

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

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  1. 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.
  2. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Interim Rationalizability," Harvard Institute of Economic Research Working Papers 2064, Harvard - Institute of Economic Research.
  3. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  4. Dirk Bergemann & Stephen Morris, 2005. "Robust Mechanism Design," Econometrica, Econometric Society, vol. 73(6), pages 1771-1813, November.
  5. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
  6. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  7. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
  8. P. Battigalli & M. Siniscalchi, 2002. "Rationalization and Incomplete Information," Princeton Economic Theory Working Papers 9817a118e65062903de7c3577, David K. Levine.
  9. Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Working Papers 2002-11, Brown University, Department of Economics.
  10. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
  11. 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.
  12. 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.
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