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Proper rationalizability and backward induction

Author

Listed:
  • Frank Schuhmacher

    () (Betriebswirtschaftliche Abteilung I, University of Bonn, Adenauerallee 24-42, D-53113 Bonn, Germany)

Abstract

This paper introduces a new normal form rationalizability concept, which in reduced normal form games corresponding to generic finite extensive games of perfect information yields the unique backward induction outcome. The basic assumption is that every player trembles "more or less rationally" as in the definition of a -proper equilibrium by Myerson (1978). In the same way that proper equilibrium refines Nash and perfect equilibrium, our model strengthens the normal form rationalizability concepts by Bernheim (1984), BÃrgers (1994) and Pearce (1984). Common knowledge of trembling implies the iterated elimination of strategies that are strictly dominated at an information set. The elimination process starts at the end of the game tree and goes backwards to the beginning.

Suggested Citation

  • Frank Schuhmacher, 1999. "Proper rationalizability and backward induction," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 599-615.
  • Handle: RePEc:spr:jogath:v:28:y:1999:i:4:p:599-615
    Note: Received: October 1996/Final version: May 1999
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    Citations

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    Cited by:

    1. Antonio Quesada, 2002. "Belief system foundations of backward induction," Theory and Decision, Springer, vol. 53(4), pages 393-403, December.
    2. Shuige Liu, 2018. "Ordered Kripke Model, Permissibility, and Convergence of Probabilistic Kripke Model," Papers 1801.08767, arXiv.org.
    3. Stephen Morris & Satoru Takahashi & Olivier Tercieux, 2012. "Robust Rationalizability Under Almost Common Certainty Of Payoffs," The Japanese Economic Review, Japanese Economic Association, vol. 63(1), pages 57-67, March.
    4. Perea, Andrés, 2011. "An algorithm for proper rationalizability," Games and Economic Behavior, Elsevier, vol. 72(2), pages 510-525, June.
    5. Perea Andrés, 2003. "Rationalizability and Minimal Complexity in Dynamic Games," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    6. Perea, Andres, 2007. "Proper belief revision and equilibrium in dynamic games," Journal of Economic Theory, Elsevier, vol. 136(1), pages 572-586, September.
    7. repec:eee:gamebe:v:104:y:2017:i:c:p:309-328 is not listed on IDEAS
    8. Asheim, Geir B., 2002. "On the epistemic foundation for backward induction," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 121-144, November.
    9. repec:spr:topjnl:v:25:y:2017:i:2:d:10.1007_s11750-017-0447-2 is not listed on IDEAS
    10. Asheim,G.B. & Perea,A., 2000. "Lexicographic probabilities and rationalizability in extensive games," Memorandum 38/2000, Oslo University, Department of Economics.
    11. Søvik, Ylva, 2009. "Strength of dominance and depths of reasoning--An experimental study," Journal of Economic Behavior & Organization, Elsevier, vol. 70(1-2), pages 196-205, May.
    12. Breitmoser, Yves & Tan, Jonathan H.W. & Zizzo, Daniel John, 2014. "On the beliefs off the path: Equilibrium refinement due to quantal response and level-k," Games and Economic Behavior, Elsevier, vol. 86(C), pages 102-125.
    13. Oikonomou, V.K. & Jost, J, 2013. "Periodic strategies and rationalizability in perfect information 2-Player strategic form games," MPRA Paper 48117, University Library of Munich, Germany.
    14. Asheim, Geir B. & Perea, Andres, 2005. "Sequential and quasi-perfect rationalizability in extensive games," Games and Economic Behavior, Elsevier, vol. 53(1), pages 15-42, October.
    15. Frick, Mira & Romm, Assaf, 2015. "Rational behavior under correlated uncertainty," Journal of Economic Theory, Elsevier, vol. 160(C), pages 56-71.
    16. Christian Bach & Andrés Perea, 2014. "Utility proportional beliefs," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 881-902, November.
    17. Shuige Liu, 2018. "Characterizing Assumption of Rationality by Incomplete Information," Papers 1801.04714, arXiv.org.
    18. Perea Andrés, 2003. "Proper Rationalizability and Belief Revision in Dynamic Games," Research Memorandum 048, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    19. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications, Elsevier.

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