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The Dynamic (In)Stability of Backwards Induction

  • R. Cressman
  • K.H. Schlag

The evolutionary basis for predicting the backwards induction solution in generic finite extensive-form games with perfect information is examined. Evolution is modelled using the replicator dynamic in combination with rare mutations that introduce a small change in the proportion of each strategy. The criterion for our judgement is whether this dynamic stabilizes over time at the subgame perfect equilibrium outcome. We find that the backwards induction solution is fully justified by this process only in simple games; simple meaning two players, two actions at each node and at most three consecutive decisions in the game. Examples of more complex games are given in which this process does not select between the subgame perfect equilibrium outcome and alternative Nash equilibrium outcomes.

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Paper provided by ESRC Centre on Economics Learning and Social Evolution in its series ELSE working papers with number 027.

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Handle: RePEc:els:esrcls:027
Contact details of provider: Web page: http://else.econ.ucl.ac.uk/
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  1. Ritzberger, Klaus & Weibull, Jörgen W., 1993. "Evolutionary Selection in Normal Form Games," Working Paper Series 383, Research Institute of Industrial Economics.
  2. Ritzberger, Klaus, 1994. "The Theory of Normal Form Games form the Differentiable Viewpoint," International Journal of Game Theory, Springer, vol. 23(3), pages 207-36.
  3. Reny Philip J., 1993. "Common Belief and the Theory of Games with Perfect Information," Journal of Economic Theory, Elsevier, vol. 59(2), pages 257-274, April.
  4. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
  5. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  6. Swinkels, J., 1991. "Evolutionary Stability with Equilibrium Entrants," Papers 9, Stanford - Institute for Thoretical Economics.
  7. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
  8. Jeroen M. Swinkels, 1991. "Adjustment Dynamics and Rational Play in Games," Discussion Papers 1001, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. van Damme, E.E.C., 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Other publications TiSEM 3734d89e-fd5c-4c80-a230-5, Tilburg University, School of Economics and Management.
  10. Ebbe Hendon & Hans Jørgen Jacobsen & Birgitte Sloth, . "Fictitious Play in Extensive Form Games," Discussion Papers 94-06, University of Copenhagen. Department of Economics.
  11. 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.
  12. 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.
  13. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
  14. 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.
  15. L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
  16. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, June.
  17. 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.
  18. Dan Friedman, 2010. "Evolutionary Games in Economics," Levine's Working Paper Archive 392, David K. Levine.
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