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Implementation by mediated equilibrium

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  • Bezalel Peleg

    ()

  • Ariel 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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File URL: http://hdl.handle.net/10.1007/s00182-009-0175-4
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Bibliographic Info

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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Related research

Keywords: Social choice; Implementation; Strong equilibrium; Mediators; Effectivity functions; Game forms;

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References

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  1. Bezalel Peleg & Ariel D. Procaccia, 2007. "Mediators Enable Truthful Voting," Discussion Paper Series dp451, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. 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.
  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, 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.
  5. Dutta, Bhaskar & Sen, Arunava, 1991. "Implementation under strong equilibrium : A complete characterization," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 49-67.
  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. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, vol. 15(1), pages 67-80.
  8. 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.
  9. Abdou, J, 1995. "Nash and Strongly Consistent Two-Player Game Forms," International Journal of Game Theory, Springer, vol. 24(4), pages 345-56.
  10. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
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