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On the outcome equivalence of backward induction and extensive form rationalizability

Author

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  • Aviad Heifetz
  • Andrés Perea

Abstract

Pearce’s (Econometrica 52:1029–1050, 1984 ) extensive-form rationalizablity (EFR) is a solution concept embodying a best-rationalization principle (Battigalli, Games Econ Behav 13:178–200, 1996 ; Battigalli and Siniscalchi, J Econ Theory 106:356–391, 2002 ) for forward-induction reasoning. EFR strategies may hence be distinct from backward-induction (BI) strategies. We provide a direct and transparent proof that, in perfect-information games with no relevant ties, the unique BI outcome is nevertheless identical to the unique EFR outcome, even when the EFR strategy profile and the BI strategy profile are distinct. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Aviad Heifetz & Andrés Perea, 2015. "On the outcome equivalence of backward induction and extensive form rationalizability," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 37-59, February.
    • Handle: RePEc:spr:jogath:v:44:y:2015:i:1:p:37-59
    DOI: 10.1007/s00182-014-0418-x
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    References listed on IDEAS

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    5. Perea, Andrés, 2014. "Belief in the opponentsʼ future rationality," Games and Economic Behavior, Elsevier, vol. 83(C), pages 231-254.
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    Cited by:

    1. Perea, Andrés, 2018. "Why forward induction leads to the backward induction outcome: A new proof for Battigalli's theorem," Games and Economic Behavior, Elsevier, vol. 110(C), pages 120-138.
    2. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    3. Arieli, Itai & Aumann, Robert J., 2015. "The logic of backward induction," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 443-464.
    4. Catonini, Emiliano, 2020. "On non-monotonic strategic reasoning," Games and Economic Behavior, Elsevier, vol. 120(C), pages 209-224.
    5. Xiao Luo & Xuewen Qian & Chen Qu, 2020. "Iterated elimination procedures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 437-465, September.
    6. Heifetz Aviad & Meier Martin & Schipper Burkhard C., 2021. "Prudent Rationalizability in Generalized Extensive-form Games with Unawareness," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 21(2), pages 525-556, June.
    7. Catonini, Emiliano, 2019. "Rationalizability and epistemic priority orderings," Games and Economic Behavior, Elsevier, vol. 114(C), pages 101-117.

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    More about this item

    Keywords

    Backward induction; Extensive-form rationalizability ; Forward induction; C72; C73;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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