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Undominated Nash Implementation in Bounded Mechanisms

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  • Matthew O. Jackson
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.

Suggested Citation

  • Matthew O. Jackson, 1990. "Undominated Nash Implementation in Bounded Mechanisms," Discussion Papers 966, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:966
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    References listed on IDEAS

    as
    1. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-134, January.
    2. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
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    5. 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 668-691, June.
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    10. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(4), pages 757-775.
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    15. Bhaskar Dutta & Arunava Sen, 1991. "A Necessary and Sufficient Condition for Two-Person Nash Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 121-128.
    16. 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.
    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.
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    19. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
    20. McKelvey, Richard D. & Niemi, Richard G., 1978. "A multistage game representation of sophisticated voting for binary procedures," Journal of Economic Theory, Elsevier, vol. 18(1), pages 1-22, June.
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