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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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References listed on IDEAS
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. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June. [Downloadable!] (restricted)
  4. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June. [Downloadable!] (restricted)
  5. 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!]
  6. 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)
  7. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March. [Downloadable!] (restricted)
  8. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September. [Downloadable!] (restricted)
  9. 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)
  10. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October. [Downloadable!] (restricted)
  11. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January. [Downloadable!] (restricted)
  12. 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)
  13. 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!]
  14. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March. [Downloadable!] (restricted)
  15. 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)
  16. 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)
  17. 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)
  18. 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)
  19. 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)
  20. 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)
  21. 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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  22. 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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  23. 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)
    Other versions:
Full references

Cited by:
(explanations, 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. Luis C. Corchon, 2007. "The theory of implementation : what did we learn?," Economics Working Papers we081207, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  2. Takashi Kunimoto, 2006. "The Robustness Of Equilibrium Analysis: The Case Of Undominated Nash Equilibrium," Departmental Working Papers 2006-26, McGill University, Department of Economics. [Downloadable!]
  3. Matthew O. Jackson & Thomas R. Palfrey, 1997. "Efficiency and Voluntary Implementation in Markets with Repeated Pairwise Bargaining," Game Theory and Information 9711003, EconWPA. [Downloadable!]
    Other versions:
  4. Walter Trockel, 1999. "On the Nash Program for the Nash Bargaining Solution," UCLA Economics Working Papers 788, UCLA Department of Economics. [Downloadable!]
  5. Matthew O. Jackson & Sanjay Srivastava, 1992. "Characterizations of Game Theoretic Solutions which Lead to Impossibility Theorems," Discussion Papers 1004, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  6. Olivier, BOCHET & Franois, MANIQUET, 2006. "Virtual Nash implementation with admissible support," Université catholique de Louvain, Département des Sciences Economiques Working Paper 2006043, Université catholique de Louvain, Département des Sciences Economiques. [Downloadable!]
  7. Akira Yamada & Naoki Yoshihara, 2008. "Mechanism design for a solution to the tragedy of commons," Review of Economic Design, Springer, vol. 11(4), pages 253-270, February. [Downloadable!] (restricted)
    Other versions:
  8. Akira Yamada & Naoki Yoshihara, 2006. "Triple Implementation by Sharing Mechanisms in Production Economies with Unequal Labor Skill," Discussion Paper Series a475, Institute of Economic Research, Hitotsubashi University. [Downloadable!]
    Other versions:
  9. Walter Trockel, 1999. "Integrating the Nash Program into Mechanism Theory," UCLA Economics Working Papers 787, UCLA Department of Economics. [Downloadable!]
  10. Hannu Vartiainen, 2007. "Subgame perfect implementation of voting rules via randomized mechanisms," Social Choice and Welfare, Springer, vol. 29(3), pages 353-367, October. [Downloadable!] (restricted)
  11. Kim-Sau Chung & Jeffrey C. Ely, 2001. "Implementation with Near-Complete Information," Discussion Papers 1332, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  12. Antonio Cabrales, 1996. "Adaptive Dynamics and the Implementation Problem with Complete Information," Economics Working Papers 179, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
    Other versions:
  13. Eiichi Miyagawa, 2002. "Subgame-perfect implementation of bargaining solutions," Discussion Papers 0102-16, Columbia University, Department of Economics. [Downloadable!]
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  14. Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 247-282, April. [Downloadable!] (restricted)
    Other versions:
  15. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics. [Downloadable!]
    Other versions:
  16. Marcelo Caffera & Juan Dubra, 2005. "Getting Polluters to Tell the Truth," Microeconomics 0504008, EconWPA. [Downloadable!]
  17. Mario Gilli, 2002. "Iterated Admissibility as Solution Concept in Game Theory," Working Papers 47, University of Milano-Bicocca, Department of Economics, revised Mar 2002. [Downloadable!]
  18. Maskin, Eric & Sjostrom, Tomas, 2001. "Implementation Theory," Working Papers 5-01-1, Pennsylvania State University, Department of Economics. [Downloadable!]
    Other versions:
  19. Hideki Mizukami & Takuma Wakayama, 2004. "Dominant Strategy Implementation in Pure Exchange Economies," Discussion Papers in Economics and Business 04-03-Rev, Osaka University, Graduate School of Economics and Osaka School of International Public Policy (OSIPP), revised Mar 2005. [Downloadable!]
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