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A general model of best response adaptation

  • Ulrich Berger

    (Vienna University of Economics)

We develop a general model of best response adaptation in large populations for symmetric and asymmetric conflicts with role-switching. For special cases including the classical best response dynamics and the symmetrized best response dynamics we show that the set of Nash equilibria is attracting for zero-sum games. For asymmetric conflicts and equally large populations, convergence to a Nash equilibrium in the base game implies convergence to a Nash equilibrium on the Wright manifold in the role game.

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File URL: http://128.118.178.162/eps/game/papers/0303/0303008.pdf
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Paper provided by EconWPA in its series Game Theory and Information with number 0303008.

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Length: 21 pages
Date of creation: 25 Mar 2003
Date of revision:
Handle: RePEc:wpa:wuwpga:0303008
Note: Type of Document - pdf-file; pages: 21; figures: included
Contact details of provider: Web page: http://128.118.178.162

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  1. Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany.
  2. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May.
  3. Ulrich Berger, 2003. "Continuous Fictitious Play via Projective Geometry," Game Theory and Information 0303004, EconWPA.
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  8. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
  9. 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.
  10. Binmore, Ken & Samuelson, Larry, 2001. "Evolution and Mixed Strategies," Games and Economic Behavior, Elsevier, vol. 34(2), pages 200-226, February.
  11. Ulrich Berger, 2002. "Best response dynamics for role games," International Journal of Game Theory, Springer, vol. 30(4), pages 527-538.
  12. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  13. Karl H. Schlag, . "Why Imitate, and if so, How? A Bounded Rational Approach to Multi- Armed Bandits," ELSE working papers 028, ESRC Centre on Economics Learning and Social Evolution.
  14. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
  15. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  16. Cressman, R., 2000. "Subgame Monotonicity in Extensive Form Evolutionary Games," Games and Economic Behavior, Elsevier, vol. 32(2), pages 183-205, August.
  17. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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