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Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics

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  • Antonio Cabrales

    (Universitat Pompeu Fabra and ELSE)

  • Giovanni Ponti

    (Universidad de Alicante and ELSE)

Abstract

This paper studies convergence and stability properties of Sjostrom's (1994) mechanism, under the assumption that boundedly rational players find their way to equilibrium using monotonic evolutionary dynamics and best-reply dynamics. This mechanism implements most social choice functions in economic environments using as a solution concept one round of deletion of weakly dominated strategies and one round of deletion of strictly dominated strategies. However, there are other sets of Nash equilibrium, whose payoffs may be very different from those desired by the social choice function. With monotonic dynamics, all these sets of equilibrium contain limit points of the evolutionary dynamics. Furthermore, even if the dynamics converge to the "right" set of equilibria (i.e., the one which contains the solution of the mechanism), it may converge to an equilibrium which is worse in welfare terms. In contrast with this result, any interior solution of the best-reply dynamics converges to the equilibrium whose outcome the planner desires. (Copyright: Elsevier)

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File URL: http://dx.doi.org/10.1006/redy.1999.0082
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Article provided by Elsevier for the Society for Economic Dynamics in its journal Review of Economic Dynamics.

Volume (Year): 3 (2000)
Issue (Month): 2 (April)
Pages: 247-282

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Handle: RePEc:red:issued:v:3:y:2000:i:2:p:247-282

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References

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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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  1. A. Roth & I. Er’ev, 2010. "Learning in Extensive Form Games: Experimental Data and Simple Dynamic Models in the Intermediate Run," Levine's Working Paper Archive 387, David K. Levine.
  2. Karl H. Schlag, 1995. "Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits," Discussion Paper Serie B, University of Bonn, Germany 361, University of Bonn, Germany, revised Mar 1996.
  3. Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 3(4), pages 367-388, December.
  4. Cressman, R., 1996. "Evolutionary Stability in the Finitely Repeated Prisoner 's Dilemma Game," Journal of Economic Theory, Elsevier, Elsevier, vol. 68(1), pages 234-248, January.
  5. R. Cressman & K.H. Schlag, . "The Dynamic (In)Stability of Backwards Induction," ELSE working papers, ESRC Centre on Economics Learning and Social Evolution 027, ESRC Centre on Economics Learning and Social Evolution.
  6. Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B, University of Bonn, Germany 296, University of Bonn, Germany.
  7. Cabrales, Antonio & Charness, Gary & Corchon, Luis C., 2003. "An experiment on Nash implementation," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 51(2), pages 161-193, June.
  8. Chen, H.-C. & Friedman, J. W. & Thisse, J.-F., . "Boundedly rational Nash equilibrium: a probabilistic choice approach," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1248, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
  10. Drew Fudenberg & David Kreps, 2010. "Learning Mixed Equilibria," Levine's Working Paper Archive 415, David K. Levine.
  11. Leslie M. Marx & Jeroen M. Swinkels, 1996. "Order Independence for Iterated Weak Dominance," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1066R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  12. Binmore, K. & Samuelson, L. & Gale, J., 1993. "Learning to be Imperfect: The Ultimatum Game," Working papers, Wisconsin Madison - Social Systems 9325, Wisconsin Madison - Social Systems.
  13. Sjostrom Tomas, 1994. "Implementation in Undominated Nash Equilibria without Integer Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 6(3), pages 502-511, May.
  14. E. Dekel & D. Fudenberg, 2010. "Rational Behavior with Payoff Uncertainty," Levine's Working Paper Archive 379, David K. Levine.
  15. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, Elsevier, vol. 71(2), pages 558-573, November.
  16. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers, Pennsylvania State - Department of Economics 11-8-2, Pennsylvania State - Department of Economics.
  17. Theodore Groves & John Ledyard, 1976. "Optimal Allocation of Public Goods: A Solution to the 'Free Rider Problem'," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 144, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  18. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, Elsevier, vol. 57(2), pages 363-391, August.
  19. Matthew, Jackson O. & Palfrey, Thomas R. & Srivastava, Sanjay., 1990. "Undominated Nash Implementation in Bounded Mechanism," Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences 754, California Institute of Technology, Division of the Humanities and Social Sciences.
  20. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
  21. Dunia López-Pintado & Giovanni Ponti, 2003. "Solomon'S Dilemma: An Experimental Study On Dynamic Implementation," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2003-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  22. Tang, Fang-Fang, 1996. "Anticipatory Learning in Two-Person Games: An Experimental Study, Part II. Learning," Discussion Paper Serie B, University of Bonn, Germany 363, University of Bonn, Germany.
  23. Giovanni Ponti, 1996. "Cycles of Learning in the Centipede Game," Discussion Papers, University College London, Department of Economics 96-22 ISSN 1350-6722, University College London, Department of Economics.
  24. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, Elsevier, vol. 64(1), pages 1-19, October.
  25. Mookherjee, Dilip & Sopher, Barry, 1997. "Learning and Decision Costs in Experimental Constant Sum Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 19(1), pages 97-132, April.
  26. Matthew 0. Jackson, 1989. "Implementation in Undominated Strategies - A Look at Bounded Mechanisms," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 833, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  27. Cooper, R. & DeJong, D.W. & Ross, T.W., 1992. "Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games," Papers, Boston University - Industry Studies Programme 36, Boston University - Industry Studies Programme.
  28. Binmore, K. & Samuelson, L., 1995. "Evolutionary Drift and Equilibrium Selection," Working papers, Wisconsin Madison - Social Systems 9529, Wisconsin Madison - Social Systems.
  29. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, Econometric Society, vol. 56(5), pages 1191-1220, September.
  30. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, Elsevier, vol. 57(2), pages 343-362, August.
  31. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, Elsevier, vol. 8(1), pages 56-90.
  32. T. Börgers, 2010. "Weak Dominance and Approximate Common Knowledge," Levine's Working Paper Archive 378, David K. Levine.
  33. De Trenqualye, Pierre, 1988. "Stability of the Groves and Ledyard mechanism," Journal of Economic Theory, Elsevier, Elsevier, vol. 46(1), pages 164-171, October.
  34. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer, Springer, vol. 19(1), pages 59-89.
  35. repec:fth:louvco:9644 is not listed on IDEAS
  36. Antonio Cabrales, . "Adaptive Dynamics and the Implementation Problem with Complete Information," ELSE working papers, ESRC Centre on Economics Learning and Social Evolution 009, ESRC Centre on Economics Learning and Social Evolution.
  37. Walker, Mark, 1981. "A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations," Econometrica, Econometric Society, Econometric Society, vol. 49(1), pages 65-71, January.
  38. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262731215, December.
  39. Vega-Redondo, Fernando, 1989. "Implementation of Lindahl equilibrium: an integration of the static and dynamic approaches," Mathematical Social Sciences, Elsevier, Elsevier, vol. 18(3), pages 211-228, December.
  40. Jordan, J. S., 1986. "Instability in the implementation of Walrasian allocations," Journal of Economic Theory, Elsevier, Elsevier, vol. 39(2), pages 301-328, August.
  41. de Trenqualye, Pierre, 1989. "Stable implementation of Lindahl allocations," Economics Letters, Elsevier, Elsevier, vol. 29(4), pages 291-294.
  42. repec:fth:calaec:16-97 is not listed on IDEAS
  43. Walker, Mark, 1984. "A simple auctioneerless mechanism with Walrasian properties," Journal of Economic Theory, Elsevier, Elsevier, vol. 32(1), pages 111-127, February.
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Citations

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Cited by:
  1. Antonio Cabrales & Roberto Serrano, 2007. "Implementation in Adaptive Better-Response Dynamics," Economics Working Papers we075731, Universidad Carlos III, Departamento de Economía.
  2. Norovsambuu Tumennasan, 2011. "To Err is Human: Implementation in Quantal Response Equilibria," Economics Working Papers, School of Economics and Management, University of Aarhus 2011-11, School of Economics and Management, University of Aarhus.
  3. Maskin, Eric & Sjostrom, Tomas, 2001. "Implementation Theory," Working Papers, Pennsylvania State University, Department of Economics 5-01-1, Pennsylvania State University, Department of Economics.
  4. Galbiati, Marco, 2008. "Fair divisions as attracting Nash equilibria of simple games," Economics Letters, Elsevier, Elsevier, vol. 100(1), pages 72-75, July.
  5. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers, Institute for Advanced Study, School of Social Science 0033, Institute for Advanced Study, School of Social Science.
  6. Cason, Timothy N. & Saijo, Tatsuyoshi & Sjostrom, Tomas & Yamato, Takehiko, 2003. "Secure Implementation Experiments: Do Strategy-proof Mechanisms Really Work?," Working Papers, Pennsylvania State University, Department of Economics 4-03-1, Pennsylvania State University, Department of Economics.
  7. Jordi Brandts & Antonio Cabrales & Gary Charness, 2007. "Forward induction and entry deterrence: an experiment," Economic Theory, Springer, Springer, vol. 33(1), pages 183-209, October.
  8. Sandholm,W.H., 1999. "Evolutionary implementation and congestion pricing," Working papers, Wisconsin Madison - Social Systems 38, Wisconsin Madison - Social Systems.
  9. Giovanni Ponti & Anita Gantner & Dunia López-Pintado & Robert Montgomery, 2003. "Solomon's Dilemma: An experimental study on dynamic implementation," Review of Economic Design, Springer, Springer, vol. 8(2), pages 217-239, October.
  10. David K. Levine & Aldo Rustichini, 2000. "Introduction," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 213-215, April.
  11. Sandholm,W.H., 2001. "Negative externalities and evolutionary implementation," Working papers, Wisconsin Madison - Social Systems 15, Wisconsin Madison - Social Systems.
  12. David K Levine & Aldo Rustichini, 2000. "Introduction: The Dynamic Games Special Issue," Levine's Working Paper Archive 2127, David K. Levine.

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