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Implementation in Mixed Nash Equilibrium

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Author Info
Claudio Mezzetti (Department of Economics, Warwick University,)
Ludovic Renou (Department of Economics, University of Leicester,)

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Abstract

A mechanism implements a social choice correspondence f in mixed Nash equilibrium if at any preference profile, the set of all pure and mixed Nash equilibrium outcomes coincides with the set of f-optimal alternatives at that preference profile. This definition generalizes Maskin’s definition of Nash implementation in that it does not require each optimal alternative to be the outcome of a pure Nash equilibrium. We show that the condition of weak set-monotonicity, a weakening of Maskin’s monotonicity, is necessary for implementation. We provide sufficient conditions for implementation and show that important social choice correspondences that are not Maskin monotonic can be implemented in mixed Nash equilibrium.

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File URL: http://www2.warwick.ac.uk/fac/soc/economics/research/papers_2009/twerp_902.pdf
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Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 902.

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Date of creation: 2009
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Handle: RePEc:wrk:warwec:902

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Related research
Keywords: implementation ; Maskin monotonicity ; pure and mixed Nash equilibrium ; weak set-monotonicity ; social choice correspondence;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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  1. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February. [Downloadable!] (restricted)
  2. Saijo, Tatsuyoshi, 1987. "On constant maskin monotonic social choice functions," Journal of Economic Theory, Elsevier, vol. 42(2), pages 382-386, August. [Downloadable!] (restricted)
  3. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-99, September. [Downloadable!] (restricted)
  4. Benoît, Jean-Pierre & Ok, Efe A., 2008. "Nash implementation without no-veto power," Games and Economic Behavior, Elsevier, vol. 64(1), pages 51-67, September. [Downloadable!] (restricted)
  5. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer, vol. 28(1), pages 111-125, January. [Downloadable!] (restricted)
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  6. Dutta, Bhaskar & Sen, Arunava, 1991. "A Necessary and Sufficient Condition for Two-Person Nash Implementation," Review of Economic Studies, Blackwell Publishing, vol. 58(1), pages 121-28, January. [Downloadable!] (restricted)
  7. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June. [Downloadable!] (restricted)
  8. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March. [Downloadable!] (restricted)
  9. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January. [Downloadable!] (restricted)
  10. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Blackwell Publishing, vol. 66(1), pages 23-38, January. [Downloadable!] (restricted)
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  11. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September. [Downloadable!] (restricted)
  12. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July. [Downloadable!] (restricted)
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  13. Kim-Sau Chung & Jeffrey C. Ely, 2003. "Implementation with Near-Complete Information," Econometrica, Econometric Society, vol. 71(3), pages 857-871, 05. [Downloadable!] (restricted)
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