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The instability of backward induction in evolutionary dynamics

  • Zibo Xu
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    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.

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    Paper provided by The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem in its series Discussion Paper Series with number dp633.

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    Length: 54 pages
    Date of creation: Jan 2013
    Date of revision:
    Handle: RePEc:huj:dispap:dp633
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    1. Ben-Porath, E., 1992. "Rationality, Nash Equilibrium and Backward Induction in Perfect Information Games," Papers 14-92, Tel Aviv - the Sackler Institute of Economic Studies.
    2. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    3. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, June.
    4. Kuzmics, Christoph, 2004. "Stochastic evolutionary stability in extensive form games of perfect information," Games and Economic Behavior, Elsevier, vol. 48(2), pages 321-336, August.
    5. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
    6. 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.
    7. Sergiu Hart, 1999. "Evolutionary Dynamics and Backward Induction," Game Theory and Information 9905002, EconWPA, revised 23 Mar 2000.
    8. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
    9. R. Cressman, K.H. Schlag, 1995. "The Dynamic (In)Stability of Backwards Induction," Discussion Paper Serie B 347, University of Bonn, Germany.
    10. Binmore, Ken, 1996. "A Note on Backward Induction," Games and Economic Behavior, Elsevier, vol. 17(1), pages 135-137, November.
    11. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, June.
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