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An Evolutionary Analysis of Bagwell's Example

  • Jorg Oechssler

    (Humboldt University, Berlin)

  • Karl Schlag

    (University of Bonn)

In a recent paper Bagwell (1995) pointed out that only the Cournot outcome, but not the Stackelberg outcome, can be supported by a pure Nash equilibrium when actions of the Stackelberg leader are observed with the slightest error. The Stackelberg outcome, however, remains close to the outcome of a mixed equilibrium. We compare the predictions in various classes of evolutionary and learning processes in this game. Only the continuous best response dynamic uniquely selects the Stackelberg outcome under noise. All other dynamics analyzed allow for the Cournot equilibrium to be selected. In typical cases Cournot is the unique long run outcome even for vanishing noise in the signal.

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Paper provided by EconWPA in its series Game Theory and Information with number 9704001.

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Date of creation: 05 Apr 1997
Date of revision: 11 Apr 1997
Handle: RePEc:wpa:wuwpga:9704001
Note: Pages: 19
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  1. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
  2. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
  3. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, June.
  4. repec:att:wimass:9325 is not listed on IDEAS
  5. Noeldecke,Georg & Samuelson,Larry, . "An evolutionary analysis of backward and forward induction," Discussion Paper Serie B 228, University of Bonn, Germany.
  6. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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  8. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
  9. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  10. van Damme, E.E.C. & Hurkens, J.P.M., 1994. "Games with imperfectly observable commitment," Discussion Paper 1994-64, Tilburg University, Center for Economic Research.
  11. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, June.
  12. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  13. Kyle Bagwell, 1992. "Commitment and Observability in Games," Discussion Papers 1014, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  14. Samuelson Larry, 1994. "Stochastic Stability in Games with Alternative Best Replies," Journal of Economic Theory, Elsevier, vol. 64(1), pages 35-65, October.
  15. Oechssler, Jorg, 1997. "An Evolutionary Interpretation of Mixed-Strategy Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 203-237, October.
  16. K. Schlag, 2010. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Levine's Working Paper Archive 454, David K. Levine.
  17. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
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