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Undominated Nash Implementation in Bounded Mechanisms

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Author Info
Matthew O. Jackson

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Abstract

We study social choice correspondences which can be implemented in undominated Nash equilibrium by bounded mechanisms. (An undominated Nash equilibrium is a Nash equilibrium in which no agent uses a weakly dominated strategy. A mechanism is bounded if every dominated strategy is dominated by an undominated strategy). We provide necessary conditions and sufficient conditions for such implementation. Our conditions are satisfied in virtually all "economic" settings, and are also satisfied by many interesting correspondences identified in the social choice literature. For economic settings, we provide a particularly simple implementing mechanism in which the undominated Nash equilibrium outcomes coincide with those obtained by iterated elimination of weakly dominated strategies.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 966.

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Date of creation: Aug 1990
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Handle: RePEc:nwu:cmsems:966

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Moulin, Herve, 1979. "Dominance Solvable Voting Schemes," Econometrica, Econometric Society, vol. 47(6), pages 1137-51, November. [Downloadable!] (restricted)
  2. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January. [Downloadable!] (restricted)
  3. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June. [Downloadable!] (restricted)
  4. Crawford, Vincent P, 1979. "A Procedure for Generating Pareto-Efficient Egalitarian-Equivalent Allocations," Econometrica, Econometric Society, vol. 47(1), pages 49-60, January. [Downloadable!] (restricted)
  5. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September. [Downloadable!] (restricted)
  6. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October. [Downloadable!] (restricted)
  7. Palfrey, Thomas R. & Srivastava, Sanjay., 1986. "Nash Implementation Using Undominated Strategies," Working Papers 649, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  8. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March. [Downloadable!] (restricted)
  9. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April. [Downloadable!] (restricted)
  10. Dutta, Bhaskar & Sen, Arunava, 1991. "A Necessary and Sufficient Condition for Two-Person Nash Implementation," Review of Economic Studies, Blackwell Publishing, vol. 58(1), pages 121-28, January. [Downloadable!] (restricted)
  11. Saijo, Tatsuyoshi, 1988. "Strategy Space Reduction in Maskin's Theorem: Sufficient Conditions for Nash Implementation," Econometrica, Econometric Society, vol. 56(3), pages 693-700, May. [Downloadable!] (restricted)
  12. Matthew 0. Jackson, 1989. "Implementation in Undominated Strategies - A Look at Bounded Mechanisms," Discussion Papers 833, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  13. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June. [Downloadable!] (restricted)
  14. Palfrey, Thomas R., 1990. "Implementation in Bayesian Equilibrium: The Multiple Equilibrium Problem in Mechanism Design," Working Papers 760, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  15. 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. [Downloadable!] (restricted)
  16. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March. [Downloadable!] (restricted)
  17. Abreu, Dilip & Sen, Arunava, 1990. "Subgame perfect implementation: A necessary and almost sufficient condition," Journal of Economic Theory, Elsevier, vol. 50(2), pages 285-299, April. [Downloadable!] (restricted)
  18. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January. [Downloadable!] (restricted)
  19. Moulin, Herve, 1994. "Social choice," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 31, pages 1091-1125 Elsevier. [Downloadable!] (restricted)
  20. 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)
  21. Palfrey, Thomas R & Srivastava, Sanjay, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Blackwell Publishing, vol. 54(2), pages 193-208, April. [Downloadable!] (restricted)
  22. Mookherjee, Dilip & Reichelstein, Stefan, 1990. "Implementation via Augmented Revelation Mechanisms," Review of Economic Studies, Blackwell Publishing, vol. 57(3), pages 453-75, July. [Downloadable!] (restricted)
  23. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July. [Downloadable!] (restricted)
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  24. 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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