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Robust Implementation: The Role of Large Type Spaces

  • Dirk Bergemann
  • Stephen Morris

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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Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 784828000000000116.

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Date of creation: 21 Jun 2005
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Handle: RePEc:cla:levrem:784828000000000116
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  1. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
  2. Stephen Morris & Dirk Bergemann, 2004. "Robust Mechanism Design," Yale School of Management Working Papers ysm380, Yale School of Management.
  3. Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February.
  4. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
  5. 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.
  6. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
  7. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  8. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Interim Rationalizability," Harvard Institute of Economic Research Working Papers 2064, Harvard - Institute of Economic Research.
  9. 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.
  10. 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.
  11. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
  12. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
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