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Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics

Author

Listed:
  • 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)

Suggested Citation

  • 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.
  • Handle: RePEc:red:issued:v:3:y:2000:i:2:p:247-282
    DOI: 10.1006/redy.1999.0082
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    Cited by:

    1. William H. Sandholm, 2002. "Evolutionary Implementation and Congestion Pricing," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 667-689.
    2. Jordi Brandts & Antonio Cabrales & Gary Charness, 2007. "Forward induction and entry deterrence: an experiment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(1), pages 183-209, October.
    3. William H. Sandholm, 2005. "Negative Externalities and Evolutionary Implementation," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 885-915.
    4. Cabrales, Antonio & Serrano, Roberto, 2011. "Implementation in adaptive better-response dynamics: Towards a general theory of bounded rationality in mechanisms," Games and Economic Behavior, Elsevier, vol. 73(2), pages 360-374.
    5. Cason, Timothy N. & Saijo, Tatsuyoshi & Sjostrom, Tomas & Yamato, Takehiko, 2006. "Secure implementation experiments: Do strategy-proof mechanisms really work?," Games and Economic Behavior, Elsevier, vol. 57(2), pages 206-235, November.
    6. Rodrigo A. Velez & Alexander L. Brown, 2018. "Empirical Equilibrium," Papers 1804.07986, arXiv.org, revised Jul 2020.
    7. Galbiati, Marco, 2008. "Fair divisions as attracting Nash equilibria of simple games," Economics Letters, Elsevier, vol. 100(1), pages 72-75, July.
    8. 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.
    9. David K Levine & Aldo Rustichini, 2000. "Introduction: The Dynamic Games Special Issue," Levine's Working Paper Archive 2127, David K. Levine.
    10. Tumennasan, Norovsambuu, 2013. "To err is human: Implementation in quantal response equilibria," Games and Economic Behavior, Elsevier, vol. 77(1), pages 138-152.
    11. Giovanni Ponti & Anita Gantner & Dunia López-Pintado & Robert Montgomery, 2003. "Solomon's Dilemma: An experimental study on dynamic implementation," Review of Economic Design, Springer;Society for Economic Design, vol. 8(2), pages 217-239, October.
    12. Rodrigo A. Velez & Alexander L. Brown, 2019. "Empirical strategy-proofness," Papers 1907.12408, arXiv.org, revised Jul 2020.
    13. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    14. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    15. Antonio Cabrales & Roberto Serrano, 2007. "Implemetation in Adaptive Better-Response Dynamics," Working Papers wp2007_0708, CEMFI.
    16. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288, Elsevier.
    17. Cason, Timothy N. & Saijo, Tatsuyoshi & Sjostrom, Tomas & Yamato, Takehiko, 2006. "Secure implementation experiments: Do strategy-proof mechanisms really work?," Games and Economic Behavior, Elsevier, vol. 57(2), pages 206-235, November.
    18. Sobel, Joel, 2019. "Iterated weak dominance and interval-dominance supermodular games," Theoretical Economics, Econometric Society, vol. 14(1), January.
    19. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.

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    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 Formulation and Implementation

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