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Adaptive Dynamics and the Implementation Problem with Complete Information

  • Cabrales, Antonio

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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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 86 (1999)
Issue (Month): 2 (June)
Pages: 159-184

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Handle: RePEc:eee:jetheo:v:86:y:1999:i:2:p:159-184
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
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  8. 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.
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  10. Walker, Mark, 1984. "A simple auctioneerless mechanism with Walrasian properties," Journal of Economic Theory, Elsevier, vol. 32(1), pages 111-127, February.
  11. 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.
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  13. Cabrales, Antonio & Sobel, Joel, 1992. "On the limit points of discrete selection dynamics," Journal of Economic Theory, Elsevier, vol. 57(2), pages 407-419, August.
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  18. 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.
  19. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
  20. Sefton, Martin & Yavas, Abdullah, 1996. "Abreu-Matsushima Mechanisms: Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 16(2), pages 280-302, October.
  21. Sjostrom, T., 1991. "Implementation in Undominated Nash Equilibria without Integer Games," Papers 491, Stockholm - International Economic Studies.
  22. De Trenqualye, Pierre, 1988. "Stability of the Groves and Ledyard mechanism," Journal of Economic Theory, Elsevier, vol. 46(1), pages 164-171, October.
  23. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
  24. Y. G. Kim & J. Sobel, 2010. "An Evolutionary Approach to Pre-play Communication," Levine's Working Paper Archive 374, David K. Levine.
  25. Binmore, Ken & Samuelson, Larry, 1996. "Evolutionary Drift and Equilibrium Selection," Economics Series 26, Institute for Advanced Studies.
  26. Binmore, K. & Samuelson, L., 1997. "Evolutionary Drift and Equilibrium Selection," Working papers 9729r, Wisconsin Madison - Social Systems.
  27. Jordan, J. S., 1986. "Instability in the implementation of Walrasian allocations," Journal of Economic Theory, Elsevier, vol. 39(2), pages 301-328, August.
  28. Glazer, Jacob & Rosenthal, Robert W, 1992. "A Note on Abreu-Matsushima Mechanisms," Econometrica, Econometric Society, vol. 60(6), pages 1435-38, November.
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