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original papers : Constitutional implementation

Author

Listed:
  • Eyal Winter

    () (Department of Economics and the Center for Rationality, The Hebrew University, Jerusalem 91905, Israel)

  • Bezalel Peleg

    () (Institute of Mathematics and the Center for Rationality and Interactive Decision Theory, The Hebrew University, Jerusalem 91904, Israel)

Abstract

We consider the problem of implementing a social choice correspondence H in Nash equilibrium when the constitution of the society is given by an effectivity function E. It is assumed that the effectivity function of $ H,E^{H}$, is a sub-correspondence of E. We found necessary and efficient conditions for a game form $\Gamma $ to implement H (in Nash equilibria), and to satisfy, at the same time, that $E^{\Gamma}$, the effectivity function of $\Gamma$, is a sub-correspondence of $E^{H}$ (which guarantees that $\Gamma$ is compatible with E). We also find sufficient conditions for the coincidence of the set of winning coalitions of $E^{\Gamma}$ and $ E^{H}$, and for $E^{\Gamma}=E^{H}$. All our results are sharp as is shown by suitable examples.

Suggested Citation

  • Eyal Winter & Bezalel Peleg, 2002. "original papers : Constitutional implementation," Review of Economic Design, Springer;Society for Economic Design, vol. 7(2), pages 187-204.
  • Handle: RePEc:spr:reecde:v:7:y:2002:i:2:p:187-204 Note: Received: 15 December 2000 / Accepted: 3 September 2001
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    References listed on IDEAS

    as
    1. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
    2. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 67-80.
    3. Jackson Matthew O. & Palfrey Thomas R. & Srivastava Sanjay, 1994. "Undominated Nash Implementation in Bounded Mechanisms," Games and Economic Behavior, Elsevier, vol. 6(3), pages 474-501, May.
    4. Saijo, Tatsuyoshi & Tatamitani, Yoshikatsu & Yamato, Takehiko, 1999. "Characterizing Natural Implementability: The Fair and Walrasian Correspondences," Games and Economic Behavior, Elsevier, vol. 28(2), pages 271-293, August.
    5. Peleg, Bezalel & Peters, Hans & Storcken, Ton, 2002. "Nash consistent representation of constitutions: a reaction to the Gibbard paradox," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 267-287, March.
    6. repec:dau:papers:123456789/13220 is not listed on IDEAS
    7. Abdou, J, 1995. "Nash and Strongly Consistent Two-Player Game Forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(4), pages 345-356.
    8. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
    9. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
    10. Dutta, Bhaskar, 1984. "Effectivity Functions and Acceptable Game Forms," Econometrica, Econometric Society, vol. 52(5), pages 1151-1166, September.
    11. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
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    Citations

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    Cited by:

    1. Joseph Abdou, 2012. "The structure of unstable power mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 389-415.
    2. Doghmi, Ahmed & Ziad, Abderrahmane, 2008. "Nash implementation in exchange economies with single-peaked preferences," Economics Letters, Elsevier, vol. 100(1), pages 157-160, July.
    3. Abdou, Joseph, 2010. "A stability index for local effectivity functions," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 306-313, May.
    4. repec:hal:journl:halshs-00331223 is not listed on IDEAS
    5. Benoit, Jean-Pierre & Ok, Efe A., 2006. "Maskin's Theorem with limited veto power," Games and Economic Behavior, Elsevier, vol. 55(2), pages 331-339, May.
    6. repec:hal:journl:halshs-00392515 is not listed on IDEAS

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