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Implementation by Mediated Equilibrium

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  • Bezalel Peleg

    ()

  • Ariel D. Procaccia

    ()

Abstract

Implementation theory tackles the following problem: given a social choice correspondence, find a decentralized mechanism such that for every constellation of the individuals' preferences, the set of outcomes in equilibrium is exactly the set of socially optimal alternatives (as specified by the correspondence). In this paper we are concerned with implementation by mediated equilibrium; under such an equilibrium, a mediator coordinates the players' strategies in a way that discourages deviation. Our main result is a complete characterization of social choice correspondences which are implementable by mediated strong equilibrium. This characterization, in addition to being strikingly concise, implies that some important social choice correspondences which are not implementable by strong equilibrium are in fact implementable by mediated strong equilibrium.

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Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp463.

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Length: 22 pages
Date of creation: Sep 2007
Date of revision:
Handle: RePEc:huj:dispap:dp463

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  1. Abdou, Joseph & Keiding, Hans, 2003. "On necessary and sufficient conditions for solvability of game forms," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 243-260, December.
  2. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, vol. 15(1), pages 67-80.
  3. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
  4. Dutta, Bhaskar & Sen, Arunava, 1991. "Implementation under strong equilibrium : A complete characterization," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 49-67.
  5. Bezalel Peleg & Ariel D. Procaccia, 2007. "Mediators Enable Truthful Voting," Discussion Paper Series dp451, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  6. Peter Fristrup & Hans Keiding, 2001. "Strongly implementable social choice correspondences and the supernucleus," Social Choice and Welfare, Springer, vol. 18(2), pages 213-226.
  7. Peleg, Bezalel, 2002. "Game-theoretic analysis of voting in committees," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 8, pages 395-423 Elsevier.
  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. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
  10. Mizutani, Masayoshi & Hiraide, Yasuhiko & Nishino, Hisakazu, 1993. "Computational Complexity to Verify the Unstability of Effectivity Function," International Journal of Game Theory, Springer, vol. 22(3), pages 225-39.
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