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Implementation, Elimination of Weakly Dominated Strategies and Evolotionary Dynamics

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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 convergence and stability prop-erties of Sjostrom's (1994) mechanism, on the assumption that boundedly rational players find their way to equilibrium using monotonic learning dynamics. 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, how-ever, many sets of Nash equilibria whose payoffs may be very different from those desired by the social choice function. We show that many equilibria in all the sets of equilibria we have described 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.

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Paper provided by ESRC Centre on Economics Learning and Social Evolution in its series ELSE working papers with number 057.

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Handle: RePEc:els:esrcls:057

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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.:
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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. Tang, Fang-Fang, 1996. "Anticipatory Learning in Two-Person Games: An Experimental Study, Part II. Learning," Discussion Paper Serie B 363, University of Bonn, Germany.
  4. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November. [Downloadable!] (restricted)
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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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  9. Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 367-388, December. [Downloadable!] (restricted)
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  13. Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December. [Downloadable!] (restricted)
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  14. Giovanni Ponti, . "Cycles Of Learning In The Centipede Game," ELSE working papers 024, ESRC Centre on Economics Learning and Social Evolution. [Downloadable!]
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  15. Walker, Mark, 1981. "A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations," Econometrica, Econometric Society, vol. 49(1), pages 65-71, January. [Downloadable!] (restricted)
  16. Barry Sopher & Dilip Mookherjee, 1997. "Learning and Decision Costs in Experimental Constant Sum Games," Departmental Working Papers 199527, Rutgers University, Department of Economics.
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  17. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October. [Downloadable!] (restricted)
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  19. Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany. [Downloadable!]
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  20. 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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  21. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July. [Downloadable!] (restricted)
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  22. 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!]
  23. 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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  25. 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)
  26. Cabrales, Antonio, 1999. "Adaptive Dynamics and the Implementation Problem with Complete Information," Journal of Economic Theory, Elsevier, vol. 86(2), pages 159-184, June. [Downloadable!] (restricted)
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  27. 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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  28. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August. [Downloadable!] (restricted)
  29. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November. [Downloadable!] (restricted)
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  33. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August. [Downloadable!] (restricted)
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  36. Borgers Tilman, 1994. "Weak Dominance and Approximate Common Knowledge," Journal of Economic Theory, Elsevier, vol. 64(1), pages 265-276, October. [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, UCLA Department of Economics. [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!]
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  5. Timothy N. Cason & Tatsuyoshi Saijo & Tomas Sjostrom & Takehiko Yamato, 2005. "Secure Implementation Experiments: Do Strategy-proof Mechanisms Really Work?," Economics Working Papers 0055, Institute for Advanced Study, School of Social Science. [Downloadable!]
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  6. 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!]
  7. repec:att:wimass:19199938 is not listed on IDEAS
  8. 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!]
  9. repec:att:wimass:1920115 is not listed on IDEAS
  10. 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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  11. 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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