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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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  • Bezalel Peleg & Ariel Procaccia, 2010. "Implementation by mediated equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 191-207, March.
    • Handle: RePEc:spr:jogath:v:39:y:2010:i:1:p:191-207
    DOI: 10.1007/s00182-009-0175-4
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    1. Dutta, Bhaskar & Sen, Arunava, 1991. "Implementation under strong equilibrium : A complete characterization," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 49-67.
    2. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
    3. Peleg,Bezalel, 2008. "Game Theoretic Analysis of Voting in Committees," Cambridge Books, Cambridge University Press, number 9780521074650.
    4. Abdou, J, 1995. "Nash and Strongly Consistent Two-Player Game Forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(4), pages 345-356.
    5. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
    6. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 67-80.
    7. Bezalel Peleg & Ariel D Procaccia, 2007. "Mediators Enable Truthful Voting," Levine's Bibliography 843644000000000039, UCLA Department of Economics.
    8. 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.
    9. repec:dau:papers:123456789/13220 is not listed on IDEAS
    10. Mizutani, Masayoshi & Hiraide, Yasuhiko & Nishino, Hisakazu, 1993. "Computational Complexity to Verify the Unstability of Effectivity Function," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 225-239.
    11. Peter Fristrup & Hans Keiding, 2001. "Strongly implementable social choice correspondences and the supernucleus," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 213-226.
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    1. Benjamin N. Roth & Ran I. Shorrer, 2021. "Making Marketplaces Safe: Dominant Individual Rationality and Applications to Market Design," Management Science, INFORMS, vol. 67(6), pages 3694-3713, June.

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