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Implementation by mediated equilibrium

  • Bezalel Peleg

    ()

  • Ariel Procaccia

    ()

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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File URL: http://hdl.handle.net/10.1007/s00182-009-0175-4
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Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 39 (2010)
Issue (Month): 1 (March)
Pages: 191-207

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Handle: RePEc:spr:jogath:v:39:y:2010:i:1:p:191-207
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  1. 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.
  2. Bezalel Peleg & Ariel D Procaccia, 2007. "Mediators Enable Truthful Voting," Levine's Bibliography 843644000000000039, UCLA Department of Economics.
  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. Abdou, J, 1995. "Nash and Strongly Consistent Two-Player Game Forms," International Journal of Game Theory, Springer, vol. 24(4), pages 345-56.
  5. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, vol. 15(1), pages 67-80.
  6. repec:cup:cbooks:9780521074650 is not listed on IDEAS
  7. Peter Fristrup & Hans Keiding, 2001. "Strongly implementable social choice correspondences and the supernucleus," Social Choice and Welfare, Springer, vol. 18(2), pages 213-226.
  8. Dutta, Bhaskar & Sen, Arunava, 1991. "Implementation under strong equilibrium : A complete characterization," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 49-67.
  9. 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.
  10. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
  11. 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.
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