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Robust Virtual Implementation

  • Dirk Bergemann
  • Stephen Morris

In a general interdependent preference environment, we characterize when two payoff types can be distinguished by their rationalizable strategic choices without any prior knowledge of their beliefs and higher order beliefs. We show that two payoff types are strategically distinguishable if and only if they satisfy a separability condition. The separability condition for each agent essentially requires that there is not too much interdependence in preferences across agents. A social choice function, mapping payoff type profiles to outcomes, can be robustly virtually implemented if there exists a mechanism such that every equilibrium on every type space achieves an outcome that is arbitrarily close to the outcome generated by the social choice function. This definition is equivalent to requiring virtual implementation in iterated deletion of strategies that are strictly dominated for all beliefs. The social choice function is robustly measurable if strategically indistinguishable payoff types receive the same allocation. We show that ex post incentive compatibility and robust measurability are necessary and sufficient for robust virtual implementation.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 814577000000000155.

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Date of creation: 27 Feb 2009
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Handle: RePEc:cla:levarc:814577000000000155
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  1. Jeffrey C. Ely & Kim-Sau Chung, 2004. "Foundations of Dominant Strategy Mechanisms," Econometric Society 2004 North American Summer Meetings 169, Econometric Society.
  2. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  3. Kim-Sau Chung & J.C. Ely, 2007. "Foundations of Dominant-Strategy Mechanisms," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 447-476.
  4. Aviad Heifetz & Zvika Neeman, 2006. "On the Generic (Im)Possibility of Full Surplus Extraction in Mechanism Design," Econometrica, Econometric Society, vol. 74(1), pages 213-233, 01.
  5. P. Battigalli & M. Siniscalchi, 2002. "Rationalization and Incomplete Information," Princeton Economic Theory Working Papers 9817a118e65062903de7c3577, David K. Levine.
  6. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-61, March.
  7. 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.
  8. 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.
  9. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
  10. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust Virtual Implementation with Incomplete Information: Toward a Reinterpretation of the Wilson Doctrine," Working Papers 2007-6, Brown University, Department of Economics.
  11. Glazer, Jacob & Rosenthal, Robert W, 1992. "A Note on Abreu-Matsushima Mechanisms," Econometrica, Econometric Society, vol. 60(6), pages 1435-38, November.
  12. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
  13. Sefton, Martin & Yavas, Abdullah, 1996. "Abreu-Matsushima Mechanisms: Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 16(2), pages 280-302, October.
  14. Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Levine's Bibliography 784828000000000116, UCLA Department of Economics.
  15. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2005. "The Limits of Ex-Post Implementation," UCLA Economics Working Papers 839, UCLA Department of Economics.
  16. Neeman, Zvika, 2004. "The relevance of private information in mechanism design," Journal of Economic Theory, Elsevier, vol. 117(1), pages 55-77, July.
  17. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-47, November.
  18. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  19. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
  20. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-92, May.
  21. Dasgupta, Partha S & Hammond, Peter J & Maskin, Eric S, 1979. "The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 185-216, April.
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