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Evolutionary dynamics may eliminate all strategies used in correlated equilibrium

  • Viossat, Yannick

We show on a 4×4 example that many dynamics may eliminate all strategies used in correlated equilibria, and this for an open set of games. This holds for the best-response dynamics, the Brown-von Neumann-Nash dynamics and any monotonic or weakly sign-preserving dynamics satisfying some standard regularity conditions. For the replicator dynamics and the best-response dynamics, elimination of all strategies used in correlated equilibrium is shown to be robust to the addition of mixed strategies as new pure strategies.

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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 56 (2008)
Issue (Month): 1 (July)
Pages: 27-43

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Handle: RePEc:eee:matsoc:v:56:y:2008:i:1:p:27-43
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  1. Ritzberger, Klaus & Weibull, Jörgen W., 1993. "Evolutionary Selection in Normal Form Games," Working Paper Series 383, Research Institute of Industrial Economics.
  2. Yannick Viossat, 2007. "The replicator dynamics does not lead to correlated equilibria," Post-Print hal-00664293, HAL.
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  7. Samuelson, L. & Zhang, J., 1990. "Evolutionary Stability In Symmetric Games," Working papers 90-24, Wisconsin Madison - Social Systems.
  8. Viossat, Yannick, 2006. "Evolutionary dynamics may eliminate all strategies used in correlated equilibrium," SSE/EFI Working Paper Series in Economics and Finance 629, Stockholm School of Economics, revised 21 Jun 2006.
  9. Ulrich Berger & Josef Hofbauer, 2004. "Irrational behavior in the Brown-von Neumann-Nash dynamics," Game Theory and Information 0409002, EconWPA, revised 09 Sep 2004.
  10. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November.
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  14. J. Swinkels, 2010. "Adjustment Dynamics and Rational Play in Games," Levine's Working Paper Archive 456, David K. Levine.
  15. Myerson, Roger B., 1994. "Communication, correlated equilibria and incentive compatibility," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 24, pages 827-847 Elsevier.
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  17. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  18. Itzhak Gilboa & Akihiko Matsui, 1991. "Social Stability and Equilibrium," Post-Print hal-00753235, HAL.
  19. Monderer, Dov & Sela, Aner, 1997. "Fictitious play and- no-cycling conditions," Sonderforschungsbereich 504 Publications 97-12, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  20. Yannick Viossat, 2008. "Is Having a Unique Equilibrium Robust?," Post-Print hal-00361891, HAL.
  21. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  22. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
  23. Yannick Viossat, 2005. "Openness of the set of games with a unique correlated equilibrium," Working Papers hal-00243016, HAL.
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  25. L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
  26. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
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