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original papers : Constitutional implementation

  • 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)

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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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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References listed on IDEAS
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  1. Dutta, Bhaskar, 1984. "Effectivity Functions and Acceptable Game Forms," Econometrica, Econometric Society, vol. 52(5), pages 1151-66, September.
  2. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, vol. 15(1), pages 67-80.
  3. Matthew O. Jackson, 1990. "Undominated Nash Implementation in Bounded Mechanisms," Discussion Papers 966, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Abdou, J, 1995. "Nash and Strongly Consistent Two-Player Game Forms," International Journal of Game Theory, Springer, vol. 24(4), pages 345-56.
  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. 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.
  7. 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.
  8. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
  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. repec:cup:cbooks:9780521074650 is not listed on IDEAS
  11. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
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