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Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics

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Author Info
Antonio Cabrales
Giovanni Ponti

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Abstract

This paper is concerned with the realism of mechanisms that implement social choice functions in the traditional sense. Will agents actually play the equilibrium assumed by the analysis? As an example, we study the convergence and stability properties of Sj\"ostr\"om's (1994) mechanism, on the assumption that boundedly rational players find their way to equilibrium using monotonic learning dynamics and also with fictitious play. This mechanism implements most social choice functions in economic environments using as a solution concept the iterated elimination of weakly dominated strategies (only one round of deletion of weakly dominated strategies is needed). There are, however, many sets of Nash equilibria whose payoffs may be very different from those desired by the social choice function. With monotonic dynamics we show that many equilibria in all the sets of equilibria we describe are the limit points of trajectories that have completely mixed initial conditions. The initial conditions that lead to these equilibria need not be very close to the limiting point. Furthermore, even if the dynamics converge to the ``right'' set of equilibria, it still can converge to quite a poor outcome in welfare terms. With fictitious play, if the agents have completely mixed prior beliefs, beliefs and play converge to the outcome the planner wants to implement.

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Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 221.

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Date of creation: Feb 1997
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Handle: RePEc:upf:upfgen:221

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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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  5. 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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  6. 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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  14. Dunia López-Pintado & Giovanni Ponti, 2003. "Solomon'S Dilemma: An Experimental Study On Dynamic Implementation," Working Papers. Serie AD 2003-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
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  15. 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)
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  34. 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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  35. 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.
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  37. 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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  38. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August. [Downloadable!] (restricted)
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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. Healy, Paul J., 2003. "Learning Dynamics in Mechanism Design: An Experimental Comparison of Public Goods Mechanisms," Working Papers 1182, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  2. David K. Levine & Aldo Rustichini, 2000. "Introduction," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 213-215, April. [Downloadable!] (restricted)
  3. David K Levine & Aldo Rustichini, 2000. "Introduction: The Dynamic Games Special Issue," Levine's Working Paper Archive 2127, David K. Levine. [Downloadable!]
  4. Antonio Cabrales & Roberto Serrano, 2007. "Implementation in adaptive better-response dynamics," Working Papers 2007-16, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales. [Downloadable!]
    Other versions:
  5. Dunia López-Pintado & Giovanni Ponti, 2003. "Solomon'S Dilemma: An Experimental Study On Dynamic Implementation," Working Papers. Serie AD 2003-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
    Other versions:
  6. Jordi Brandts & Antonio Cabrales & Gary Charness, 2007. "Forward induction and entry deterrence: an experiment," Economic Theory, Springer, vol. 33(1), pages 183-209, October. [Downloadable!] (restricted)
  7. Tatsuyoshi Saijo & Timothy N. Cason & Tomas Sjostrom, 2003. "Secure Implementation Experiments:Do Strategy-proof Mechanisms Really Work?," Discussion papers 03012, Research Institute of Economy, Trade and Industry (RIETI). [Downloadable!]
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  8. 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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  9. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science. [Downloadable!]
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  10. 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!]
  11. repec:att:wimass:19199938 is not listed on IDEAS
  12. repec:att:wimass:1920115 is not listed on IDEAS
  13. Marco Galbiati, 2006. "Fair Divisions as Attracting Nash Equilibria of Simple Games," Economics Working Papers ECO2006/24, European University Institute. [Downloadable!]
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