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original papers : Constitutional implementation

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Author Info

  • 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.

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Bibliographic Info

Article provided by Springer in its journal Review of Economic Design.

Volume (Year): 7 (2002)
Issue (Month): 2 ()
Pages: 187-204

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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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Related research

Keywords: Implementation; Nash equilibrium; effectivity function;

References

References listed on IDEAS
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  1. 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.
  2. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
  3. Peleg,Bezalel, 2008. "Game Theoretic Analysis of Voting in Committees," Cambridge Books, Cambridge University Press, number 9780521074650, October.
  4. 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.
  5. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
  6. 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.
  7. Dutta, Bhaskar, 1984. "Effectivity Functions and Acceptable Game Forms," Econometrica, Econometric Society, vol. 52(5), pages 1151-66, September.
  8. Abdou, J, 1995. "Nash and Strongly Consistent Two-Player Game Forms," International Journal of Game Theory, Springer, vol. 24(4), pages 345-56.
  9. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, vol. 15(1), pages 67-80.
  10. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
  11. 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.
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Citations

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Cited by:
  1. repec:hal:cesptp:halshs-00389003 is not listed on IDEAS
  2. repec:hal:cesptp:halshs-00331223 is not listed on IDEAS
  3. Joseph Abdou, 2008. "A stability index for local effectivity functions," Documents de travail du Centre d'Economie de la Sorbonne b08056, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  4. repec:hal:journl:halshs-00392515 is not listed on IDEAS
  5. repec:hal:journl:halshs-00389003 is not listed on IDEAS
  6. repec:hal:journl:halshs-00331223 is not listed on IDEAS
  7. repec:hal:wpaper:halshs-00389181 is not listed on IDEAS
  8. Doghmi, Ahmed & Ziad, Abderrahmane, 2008. "Nash implementation in exchange economies with single-peaked preferences," Economics Letters, Elsevier, vol. 100(1), pages 157-160, July.
  9. Joseph Abdou, 2012. "The structure of unstable power mechanisms," Economic Theory, Springer, vol. 50(2), pages 389-415, June.

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