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Evolutionary dynamics may eliminate all strategies used in correlated equilibrium

In (Viossat, 2006, "The replicator dynamics does not lead to correlated equilibria", forthcoming in Games and Economic Behavior), it was shown that the replicator dynamics may eliminate all pure strategies used in correlated equilibrium, so that only strategies that do not take part in any correlated equilibrium remain. Here, we generalize this result by showing that it holds for an open set of games, and for many other dynamics, including 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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File URL: http://swopec.hhs.se/hastef/papers/hastef0629.pdf
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Paper provided by Stockholm School of Economics in its series SSE/EFI Working Paper Series in Economics and Finance with number 629.

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Length: 34 pages
Date of creation: 15 May 2006
Date of revision: 21 Jun 2006
Handle: RePEc:hhs:hastef:0629
Note: The first version was called "Evolutionary dynamics do no lead to correlated equilibria"
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  1. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May.
  2. Viossat, Yannick, 2008. "Is having a unique equilibrium robust?," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1152-1160, December.
  3. Berger, Ulrich & Hofbauer, Josef, 2006. "Irrational behavior in the Brown-von Neumann-Nash dynamics," Games and Economic Behavior, Elsevier, vol. 56(1), pages 1-6, July.
  4. 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.
  5. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
  6. Sergiu Hart, 2004. "Adaptive Heuristics," Discussion Paper Series dp372, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  7. Samuelson, L. & Zhang, J., 1990. "Evolutionary Stability In Symmetric Games," Working papers 90-24, Wisconsin Madison - Social Systems.
  8. J. Swinkels, 2010. "Adjustment Dynamics and Rational Play in Games," Levine's Working Paper Archive 456, David K. Levine.
  9. Viossat, Yannick, 2007. "The replicator dynamics does not lead to correlated equilibria," Games and Economic Behavior, Elsevier, vol. 59(2), pages 397-407, May.
  10. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
  11. Sergiu Hart & Andreu Mas-Colell, 2001. "Regret-Based Continuous-Time Dynamics," Discussion Paper Series dp309, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised Apr 2003.
  12. 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.
  13. AUMANN, Robert J., . "Subjectivity and correlation in randomized strategies," CORE Discussion Papers RP -167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Yannick Viossat, 2005. "Openness of the set of games with a unique correlated equilibrium," Working Papers hal-00243016, HAL.
  15. K. Ritzberger & J. Weibull, 2010. "Evolutionary Selection in Normal-Form Games," Levine's Working Paper Archive 452, David K. Levine.
  16. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
  17. A. Gaunersdorfer & J. Hofbauer, 2010. "Fictitious Play, Shapley Polygons and the Replicator Equation," Levine's Working Paper Archive 438, David K. Levine.
  18. L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
  19. 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.
  20. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  21. 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.
  22. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181, March.
  23. Dan Friedman, 2010. "Evolutionary Games in Economics," Levine's Working Paper Archive 392, David K. Levine.
  24. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
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