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Proper rationalizability and backward induction

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  • Frank Schuhmacher

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

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    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.

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    Bibliographic Info

    Article provided by Springer in its journal International Journal of Game Theory.

    Volume (Year): 28 (1999)
    Issue (Month): 4 ()
    Pages: 599-615

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    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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    Web page: http://link.springer.de/link/service/journals/00182/index.htm

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    Related research

    Keywords: Rationalizability · backward induction · normal form;

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    Cited by:
    1. Perea, Andrés, 2011. "An algorithm for proper rationalizability," Games and Economic Behavior, Elsevier, vol. 72(2), pages 510-525, June.
    2. 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.
    3. Perea, Andres, 2007. "Proper belief revision and equilibrium in dynamic games," Journal of Economic Theory, Elsevier, vol. 136(1), pages 572-586, September.
    4. Asheim,G.B., 1999. "On the epistemic foundation for backward induction," Memorandum 30/1999, Oslo University, Department of Economics.
    5. Yves Breitmoser & Jonathan H.W. Tan & Daniel John Zizzo, 2010. "On the Beliefs off the Path: Equilibrium Refinement due to Quantal Response and Level-k," ICBBR Working Papers 9, International Centre for Behavioural Business Research.
    6. 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).
    7. Antonio Quesada, 2002. "Belief system foundations of backward induction," Theory and Decision, Springer, vol. 53(4), pages 393-403, December.
    8. 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.
    9. 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).

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