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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 mechanisms 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 implementation with refined equilibrium concepts have claimed that the mechanisms they propose are ``simple'' and implement ``everything'' (in contrast with the canonical mechanism). The fact that some of these ``simple'' mechanisms have unstable equilibria suggests that these statements should be interpreted with some caution.

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Bibliographic Info

Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 179.

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Date of creation: Jul 1996
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Handle: RePEc:upf:upfgen:179

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Web page: http://www.econ.upf.edu/

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Keywords: Implementation; bounded rationality; evolutionary dynamics; mechanisms;

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  1. Jackson, Matthew O, 1992. "Implementation in Undominated.Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 59(4), pages 757-75, October.
  2. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-42, November.
  3. Walker, Mark, 1984. "A simple auctioneerless mechanism with Walrasian properties," Journal of Economic Theory, Elsevier, vol. 32(1), pages 111-127, February.
  4. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
  5. Antonio Cabrales & Joel Sobel, 2010. "On the Limit Points of Discrete Selection Dynamics," Levine's Working Paper Archive 432, David K. Levine.
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  7. 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.
  8. L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
  9. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
  10. Y. G. Kim & J. Sobel, 2010. "An Evolutionary Approach to Pre-play Communication," Levine's Working Paper Archive 374, David K. Levine.
  11. Binmore, K. & Samuelson, L., 1997. "Evolutionary Drift and Equilibrium Selection," Working papers 9729r, Wisconsin Madison - Social Systems.
  12. Dasgupta, Partha S & Hammond, Peter J & Maskin, Eric S, 1979. "The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 185-216, April.
  13. De Trenqualye, Pierre, 1988. "Stability of the Groves and Ledyard mechanism," Journal of Economic Theory, Elsevier, vol. 46(1), pages 164-171, October.
  14. Kim, Yong-Gwan & Sobel, Joel, 1995. "An Evolutionary Approach to Pre-play Communication," Econometrica, Econometric Society, vol. 63(5), pages 1181-93, September.
  15. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
  16. Sefton, Martin & Yavas, Abdullah, 1996. "Abreu-Matsushima Mechanisms: Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 16(2), pages 280-302, October.
  17. Sjostrom, T., 1991. "Implementation in Undominated Nash Equilibria without Integer Games," Papers 491, Stockholm - International Economic Studies.
  18. de Trenqualye, Pierre, 1989. "Stable implementation of Lindahl allocations," Economics Letters, Elsevier, vol. 29(4), pages 291-294.
  19. Glazer, Jacob & Rosenthal, Robert W, 1992. "A Note on Abreu-Matsushima Mechanisms," Econometrica, Econometric Society, vol. 60(6), pages 1435-38, November.
  20. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
  21. Vega-Redondo, Fernando, 1989. "Implementation of Lindahl equilibrium: an integration of the static and dynamic approaches," Mathematical Social Sciences, Elsevier, vol. 18(3), pages 211-228, December.
  22. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  23. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  24. Jordan, J. S., 1986. "Instability in the implementation of Walrasian allocations," Journal of Economic Theory, Elsevier, vol. 39(2), pages 301-328, August.
  25. 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.
  26. Groves, Theodore & Ledyard, John O, 1977. "Optimal Allocation of Public Goods: A Solution to the "Free Rider" Problem," Econometrica, Econometric Society, vol. 45(4), pages 783-809, May.
  27. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
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