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The Dynamic (In)Stability of Backwards Induction

  • Cressman, R.
  • Schlag, K. H.

The analysis of the replicator dynamic in generic perfect information games yields the following results. In the long run, players play a Nash equilibrium provided that initially all strategies are present. There is at most one ``stable'' component (formally, an interior asymptotically stable set), play in this component will follow the backwards induction path. Existence of such a component is guaranteed in games with at most three consecutive decision nodes. An example of a ``longer'' game is provided where some trajectories starting close to the backwards induction component lead away and never come back.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 83 (1998)
Issue (Month): 2 (December)
Pages: 260-285

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Handle: RePEc:eee:jetheo:v:83:y:1998:i:2:p:260-285
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Ebbe Hendon & Hans Jørgen Jacobsen & Birgitte Sloth, . "Fictitious Play in Extensive Form Games," Discussion Papers 94-06, University of Copenhagen. Department of Economics.
  2. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, June.
  3. Swinkels, Jeroen M., 1992. "Evolutionary stability with equilibrium entrants," Journal of Economic Theory, Elsevier, vol. 57(2), pages 306-332, August.
  4. L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
  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. 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.
  7. Dan Friedman, 2010. "Evolutionary Games in Economics," Levine's Working Paper Archive 392, David K. Levine.
  8. K. Ritzberger & J. Weibull, 2010. "Evolutionary Selection in Normal-Form Games," Levine's Working Paper Archive 452, David K. Levine.
  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. J. Swinkels, 2010. "Adjustment Dynamics and Rational Play in Games," Levine's Working Paper Archive 456, David K. Levine.
  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. 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.
  13. 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.
  14. KOHLBERG, Elon & MERTENS, Jean-François, . "On the strategic stability of equilibria," CORE Discussion Papers RP -716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. 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.
  16. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
  17. 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.
  18. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
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