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Adaptive Dynamics and the Implementation Problem with Complete Information

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  • Antonio Cabrales

Abstract

This paper studies the equilibrating process of several implementation mecha-nisms using naive adaptive dynamics. We show that the dynamics converge and are stable, for the canonical mechanism of implementation in Nash equilibrium. In this way we cast some doubt on the criticism of complexity commonly used against this mechanism. For mechanisms that use more refined equilibrium concepts, the dynamics converge but are not stable. Some papers in the literature on implemen-tation with refined equilibrium concepts have claimed that the mechanisms they propose are simple and implement everything (in contrast with the canoni-cal mechanism). The fact that some of these simple mechanisms have unstable equilibria suggests that these statements should be interpreted with some caution. Key Words: Implementation; Bounded Rationality; Evolutionary dynamics; Mechanisms.

Suggested Citation

  • Antonio Cabrales, "undated". "Adaptive Dynamics and the Implementation Problem with Complete Information," ELSE working papers 009, ESRC Centre on Economics Learning and Social Evolution.
    • Handle: RePEc:els:esrcls:009
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    Cited by:

    1. William H. Sandholm, 2002. "Evolutionary Implementation and Congestion Pricing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 667-689.
    2. Hitoshi Matsushima, 2002. "Honesty-Proof Implementation," CIRJE F-Series CIRJE-F-178, CIRJE, Faculty of Economics, University of Tokyo.
    3. repec:cdl:ucsbec:6-98 is not listed on IDEAS
    4. William H. Sandholm, 2005. "Negative Externalities and Evolutionary Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 885-915.
    5. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    6. 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.
    7. Corchón, Luis C., 2008. "The theory of implementation : what did we learn?," UC3M Working papers. Economics we081207, Universidad Carlos III de Madrid. Departamento de Economía.
    8. 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.
    9. Galbiati, Marco, 2008. "Fair divisions as attracting Nash equilibria of simple games," Economics Letters, Elsevier, vol. 100(1), pages 72-75, July.
    10. Mathevet, Laurent & Taneva, Ina, 2013. "Finite supermodular design with interdependent valuations," Games and Economic Behavior, Elsevier, vol. 82(C), pages 327-349.
    11. Tumennasan, Norovsambuu, 2013. "To err is human: Implementation in quantal response equilibria," Games and Economic Behavior, Elsevier, vol. 77(1), pages 138-152.
    12. Meng, Dawen & Tian, Guoqiang, 2013. "Entry-Deterring Nonlinear Pricing with Bounded Rationality," MPRA Paper 57935, University Library of Munich, Germany, revised May 2014.
    13. Javier Rivas Ruiz, 2014. "Mechanism Design and Robust Control," Department of Economics Working Papers 22/14, University of Bath, Department of Economics.
    14. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    15. DavidP. Myatt & Chris Wallace, 2009. "Evolution, Teamwork and Collective Action: Production Targets in the Private Provision of Public Goods," Economic Journal, Royal Economic Society, vol. 119(534), pages 61-90, January.
    16. Saran, Rene, 2016. "Bounded depths of rationality and implementation with complete information," Journal of Economic Theory, Elsevier, vol. 165(C), pages 517-564.
    17. Rivas, Javier, 2015. "Mechanism design and bounded rationality: The case of type misreporting," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 6-13.
    18. Antonio Cabrales & Roberto Serrano, 2007. "Implemetation in Adaptive Better-Response Dynamics," Working Papers wp2007_0708, CEMFI.
    19. Sobel, Joel, 2000. "Economists' Models of Learning," Journal of Economic Theory, Elsevier, vol. 94(2), pages 241-261, October.
    20. Accinelli, Elvio & Martins, Filipe & Pinto, Alberto A., 2020. "Evolutionary dynamics for the generalized Baliga–Maskin public good model," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    21. 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.
    22. Cabrales, Antonio & Charness, Gary & Corchon, Luis C., 2003. "An experiment on Nash implementation," Journal of Economic Behavior & Organization, Elsevier, vol. 51(2), pages 161-193, June.
    23. Hitoshi Matsushima, 2002. "Stability and Implementation via Simple Mechanisms in the Complete Information Environments," CIRJE F-Series CIRJE-F-147, CIRJE, Faculty of Economics, University of Tokyo.
    24. , J. & ,, 2012. "Designing stable mechanisms for economic environments," Theoretical Economics, Econometric Society, vol. 7(3), September.
    25. 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.;
    All these keywords.

    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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