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Robust Virtual Implementation

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Author Info
Dirk Bergemann () (Cowles Foundation, Yale University)
Stephen Morris (Dept. of Economics, Princeton University)

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Abstract

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 arbitrarily close to 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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File URL: http://cowles.econ.yale.edu/P/cd/d16a/d1609-rr.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1609RR.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 53 pages
Date of creation: Jun 2007
Date of revision: Jan 2009
Publication status: Published in Theoretical Economics (2009), 4: 45-88
Handle: RePEc:cwl:cwldpp:1609rr

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

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Related research
Keywords: Mechanism design; Virtual implementation; Robust implementation; Rationaliz­ability; Ex-post incentive compatibility;

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Find related papers by JEL classification:
C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information

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References listed on IDEAS
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    Other versions:
  2. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June. [Downloadable!] (restricted)
  3. Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Cowles Foundation Discussion Papers 1519, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  4. 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. [Downloadable!]
  5. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2006. "The Limits of ex post Implementation," Econometrica, Econometric Society, vol. 74(3), pages 585-610, 05. [Downloadable!] (restricted)
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  6. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-92, May.
  7. Jackson, Matthew O, 1992. "Implementation in Undominated.Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Blackwell Publishing, vol. 59(4), pages 757-75, October. [Downloadable!] (restricted)
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  8. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July. [Downloadable!] (restricted)
  9. Sefton, Martin & Yavas, Abdullah, 1996. "Abreu-Matsushima Mechanisms: Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 16(2), pages 280-302, October. [Downloadable!] (restricted)
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  12. 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. [Downloadable!] (restricted)
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  14. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March. [Downloadable!] (restricted)
  15. 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, Blackwell Publishing, vol. 46(2), pages 185-216, April. [Downloadable!] (restricted)
  16. Pierpaolo Battigalli & Marciano Siniscalchi, 2003. "Rationalization and Incomplete Information," Advances in Theoretical Economics, Berkeley Electronic Press, vol. 3(1), pages 1073-1073. [Downloadable!] (restricted)
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  17. Neeman, Zvika, 2004. "The relevance of private information in mechanism design," Journal of Economic Theory, Elsevier, vol. 117(1), pages 55-77, July. [Downloadable!] (restricted)
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  18. Battigalli, P., 1999. "Rationalizability in Incomplete Information Games," Economics Working Papers eco99/17, European University Institute.
  19. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November. [Downloadable!] (restricted)
  20. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September. [Downloadable!] (restricted)
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  21. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust virtual implementation with incomplete information: Towards a reinterpretation of the Wilson doctrine," Working Papers 2007-14, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales. [Downloadable!]
    Other versions:
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