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Adaptive Dynamics and the Implementation Problem with Complete Information

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Author Info
Antonio Cabrales

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Abstract

This paper studies the equilibrating process of several implementation mechanisms using naive adaptive dynamics. We show that the dynamics converge and are stable, for the canonical mechanism of implementation in Nash equilibrium. In this way we cast some doubt on the criticism of ``complexity'' commonly used against this mechanism. For mechanisms that use more refined equilibrium concepts, the dynamics converge but are not stable. Some papers in the literature on implementation with refined equilibrium concepts have claimed that the mechanisms they propose are ``simple'' and implement ``everything'' (in contrast with the canonical mechanism). The fact that some of these ``simple'' mechanisms have unstable equilibria suggests that these statements should be interpreted with some caution.

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Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 179.

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Date of creation: Jul 1996
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Handle: RePEc:upf:upfgen:179

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Related research
Keywords: Implementation; bounded rationality; evolutionary dynamics; mechanisms;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy-Making and Implementation

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References listed on IDEAS
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  1. Groves, Theodore & Ledyard, John O, 1977. "Optimal Allocation of Public Goods: A Solution to the "Free Rider" Problem," Econometrica, Econometric Society, vol. 45(4), pages 783-809, May. [Downloadable!] (restricted)
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  2. Samuelson, L. & Zhang, J., 1991. "Evolutionary Stability in Asymmetric Games," Papers 9132, Tilburg - Center for Economic Research.
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  3. Sjostrom Tomas, 1994. "Implementation in Undominated Nash Equilibria without Integer Games," Games and Economic Behavior, Elsevier, vol. 6(3), pages 502-511, May. [Downloadable!] (restricted)
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  4. Jackson, Matthew O, 1992. "Implementation in Undominated.Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Blackwell Publishing, vol. 59(4), pages 757-75, October. [Downloadable!] (restricted)
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  5. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September. [Downloadable!] (restricted)
  6. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October. [Downloadable!] (restricted)
  7. De Trenqualye, Pierre, 1988. "Stability of the Groves and Ledyard mechanism," Journal of Economic Theory, Elsevier, vol. 46(1), pages 164-171, October. [Downloadable!] (restricted)
  8. Kim, Yong-Gwan & Sobel, Joel, 1995. "An Evolutionary Approach to Pre-play Communication," Econometrica, Econometric Society, vol. 63(5), pages 1181-93, September. [Downloadable!] (restricted)
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  9. Cabrales, Antonio & Sobel, Joel, 1992. "On the limit points of discrete selection dynamics," Journal of Economic Theory, Elsevier, vol. 57(2), pages 407-419, August. [Downloadable!] (restricted)
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  10. repec:att:wimass:199529 is not listed on IDEAS
  11. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August. [Downloadable!] (restricted)
  12. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May. [Downloadable!] (restricted)
  13. Binmore, Ken & Samuelson, Larry, 1996. "Evolutionary Drift and Equilibrium Selection," Economics Series 26, Institute for Advanced Studies. [Downloadable!]
  14. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November. [Downloadable!] (restricted)
  15. Jackson Matthew O. & Palfrey Thomas R. & Srivastava Sanjay, 1994. "Undominated Nash Implementation in Bounded Mechanisms," Games and Economic Behavior, Elsevier, vol. 6(3), pages 474-501, May. [Downloadable!] (restricted)
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  16. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer, vol. 19(1), pages 59-89.
  17. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September. [Downloadable!] (restricted)
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Antonio Cabrales & Roberto Serrano, 2007. "Implementation in adaptive better-response dynamics," Working Papers 2007-16, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales. [Downloadable!]
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  2. Hitoshi Matsushima, 2002. "Honesty-Proof Implementation," CIRJE F-Series CIRJE-F-178, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  3. Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 247-282, April. [Downloadable!] (restricted)
    Other versions:
  4. Hitoshi Matsushima, 2002. "Stability and Implementation via Simple Mechanisms in the Complete Information Environments," CIRJE F-Series CIRJE-F-147, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  5. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics. [Downloadable!]
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  6. Antonio Cabrales & Gary Charness & Luis Corchón, 1998. "An Experiment on Nash Implementation," Economics Working Papers 300, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
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  7. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science. [Downloadable!]
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  8. Luis C. Corchon, 2007. "The theory of implementation : what did we learn?," Economics Working Papers we081207, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  9. Mathevet, Laurent, 2007. "Supermodular Bayesian implementation: Learning and incentive design," Working Papers 1265, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  10. repec:att:wimass:19199938 is not listed on IDEAS
  11. repec:att:wimass:1920115 is not listed on IDEAS
  12. Marco Galbiati, 2006. "Fair Divisions as Attracting Nash Equilibria of Simple Games," Economics Working Papers ECO2006/24, European University Institute. [Downloadable!]
    Other versions:
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