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Implementation, elimination of weakly dominated strategies and evolutionary dynamics

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  • Antonio Cabrales
  • Giovanni Ponti

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.

Suggested Citation

  • Antonio Cabrales & Giovanni Ponti, 1997. "Implementation, elimination of weakly dominated strategies and evolutionary dynamics," Economics Working Papers 221, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:221
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    References listed on IDEAS

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    Citations

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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.
    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. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    13. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
    14. Roberto Serrano & Antonio Cabrales, 2007. "Implementation in Adaptive Better-Response Dynamics," Working Papers 2007-10, Brown University, Department of Economics.
    15. 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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    More about this item

    Keywords

    Implementation; bounded rationality; evolutionary dynamics; mechanisms;

    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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