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Loss of Commitment? An Evolutionary Analysis of Bagwell’s Example

  • Jörg Oechssler
  • Karl H Schlag

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 David K. Levine in its series Levine's Working Paper Archive with number 598.

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Date of creation: 14 May 1997
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Handle: RePEc:cla:levarc:598
Contact details of provider: Web page: http://www.dklevine.com/

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  1. Gueth, Werner & Kirchsteiger, Georg & Ritzberger, Klaus, 1996. "Imperfectly Observable Commitments in n-Player Games," Economics Series 35, Institute for Advanced Studies.
  2. Noldeke Georg & Samuelson Larry, 1993. "An Evolutionary Analysis of Backward and Forward Induction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 425-454, July.
  3. Cressman, R. & Schlag, K. H., 1998. "The Dynamic (In)Stability of Backwards Induction," Journal of Economic Theory, Elsevier, vol. 83(2), pages 260-285, December.
  4. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  5. Karl H. Schlag, 1995. "Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits," Discussion Paper Serie B 361, University of Bonn, Germany, revised Mar 1996.
  6. Bagwell, Kyle, 1995. "Commitment and observability in games," Games and Economic Behavior, Elsevier, vol. 8(2), pages 271-280.
  7. L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
  8. van Damme, Eric & Hurkens, Sjaak, 1997. "Games with Imperfectly Observable Commitment," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 282-308, October.
  9. Dan Friedman, 2010. "Evolutionary Games in Economics," Levine's Working Paper Archive 392, David K. Levine.
  10. B. Adolph, 1996. "Commitment, Trembling Hand Imperfection and Observability in Games," SFB 373 Discussion Papers 1996,84, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  11. Joerg Oechssler, 1994. "An Evolutionary Interpretation Of Mixed-Strategy Equilibria," Game Theory and Information 9404001, EconWPA.
  12. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
  13. 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.
  14. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
  15. 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.
  16. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  17. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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