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Evolutionary Dynamics May Eliminate All Strategies Used in Correlated Equilibria

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  • Viossat, Yannick

Abstract

We show on a 4x4 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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Bibliographic Info

Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/1119.

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Date of creation: Jul 2008
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Publication status: Published in Mathematical Social Sciences, 2008, Vol. 56, no. 1. pp. 27-43.Length: 16 pages
Handle: RePEc:dau:papers:123456789/1119

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Related research

Keywords: Correlated equilibrium; Evolutionary dynamics; Elimination; As-if rationality;

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References

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  1. 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.
  2. Sergiu Hart, 2004. "Adaptive Heuristics," Levine's Bibliography 122247000000000471, UCLA Department of Economics.
  3. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  4. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May.
  5. J. Swinkels, 2010. "Adjustment Dynamics and Rational Play in Games," Levine's Working Paper Archive 456, David K. Levine.
  6. Dan Friedman, 2010. "Evolutionary Games in Economics," Levine's Working Paper Archive 392, David K. Levine.
  7. Sergiu Hart & Andreu Mas-Colell, 2001. "Regret-Based Continuous-Time Dynamics," Discussion Paper Series dp309, The Center for the Study of Rationality, Hebrew University, Jerusalem, revised Apr 2003.
  8. L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
  9. Samuelson, L. & Zhang, J., 1991. "Evolutionary Stability in Asymmetric Games," Papers 9132, Tilburg - Center for Economic Research.
  10. 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.
  11. 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).
  12. Viossat, Yannick, 2008. "Is Having a Unique Equilibrium Robust?," Economics Papers from University Paris Dauphine 123456789/387, Paris Dauphine University.
  13. 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.
  14. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181, September.
  15. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
  16. Yannick Viossat, 2008. "Evolutionary Dynamics May Eliminate All Strategies Used in Correlated Equilibria," Post-Print hal-00360756, HAL.
  17. A. Gaunersdorfer & J. Hofbauer, 2010. "Fictitious Play, Shapley Polygons and the Replicator Equation," Levine's Working Paper Archive 438, David K. Levine.
  18. 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.
  19. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  20. Viossat, Yannick, 2007. "The replicator dynamics does not lead to correlated equilibria," Games and Economic Behavior, Elsevier, vol. 59(2), pages 397-407, May.
  21. K. Ritzberger & J. Weibull, 2010. "Evolutionary Selection in Normal-Form Games," Levine's Working Paper Archive 452, David K. Levine.
  22. Yannick Viossat, 2005. "Openness of the set of games with a unique correlated equilibrium," Working Papers hal-00243016, HAL.
  23. 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.
  24. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
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Citations

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Cited by:
  1. Viossat, Yannick, 2008. "Evolutionary dynamics may eliminate all strategies used in correlated equilibrium," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 27-43, July.
  2. Russell Golman, 2011. "Why learning doesn’t add up: equilibrium selection with a composition of learning rules," International Journal of Game Theory, Springer, vol. 40(4), pages 719-733, November.
  3. Yannick Viossat, 2012. "Game Dynamics and Nash Equilibria," Working Papers hal-00756096, HAL.
  4. Yannick Viossat, 2011. "Deterministic monotone dynamics and dominated strategies," Working Papers hal-00636620, HAL.
  5. Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, vol. 2(1), pages 160-175, March.

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