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Undominated Nash Implementation in Bounded Mechanisms

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  • Jackson Matthew O.
  • Palfrey Thomas R.
  • Srivastava Sanjay

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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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 6 (1994)
Issue (Month): 3 (May)
Pages: 474-501

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Handle: RePEc:eee:gamebe:v:6:y:1994:i:3:p:474-501

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Palfrey, Thomas R & Srivastava, Sanjay, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Wiley Blackwell, vol. 54(2), pages 193-208, April.
  2. 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.
  3. 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.
  4. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
  5. 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.
  6. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
  7. Mookherjee, Dilip & Reichelstein, Stefan, 1990. "Implementation via Augmented Revelation Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 57(3), pages 453-75, July.
  8. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  9. Dutta, Bhaskar & Sen, Arunava, 1991. "A Necessary and Sufficient Condition for Two-Person Nash Implementation," Review of Economic Studies, Wiley Blackwell, vol. 58(1), pages 121-28, January.
  10. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January.
  11. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  12. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March.
  13. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
  14. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
  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.
  16. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  17. Moulin, Herve, 1979. "Dominance Solvable Voting Schemes," Econometrica, Econometric Society, vol. 47(6), pages 1137-51, November.
  18. 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.
  19. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
  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, Wiley Blackwell, vol. 46(2), pages 185-216, April.
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