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The instability of backward induction in evolutionary dynamics


  • Zibo Xu


This paper continues the work initiated in [19]. We adopt the same model as in [19]. We show that the non-backward-induction equilibrium component may be evolutionarily stable for any population size in a finite stopping game where the two equilibrium components are terminated by different players. A surprising result is that the backward induction equilibrium component may not be evolutionarily stable for large populations. Finally, we study the evolutionary stability result in a different limiting process where the expected number of mutations per generation is bounded away from both zero and infinity.

Suggested Citation

  • Zibo Xu, 2013. "The instability of backward induction in evolutionary dynamics," Discussion Paper Series dp633, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp633

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    References listed on IDEAS

    1. Elchanan Ben-Porath, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," Review of Economic Studies, Oxford University Press, vol. 64(1), pages 23-46.
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    7. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    8. Binmore, Ken, 1996. "A Note on Backward Induction," Games and Economic Behavior, Elsevier, vol. 17(1), pages 135-137, November.
    9. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, July.
    10. 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.
    11. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, July.
    12. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
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