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The Logic of Backward Induction

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  • Itai Arieli
  • Robert J. Aumann

Abstract

The logic of backward induction (BI) in perfect information (PI) games has been intensely scrutinized for the past quarter century. A major development came in 2002, when P. Battigalli and M. Sinischalchi (BS) showed that an outcome of a PI game is consistent with common strong belief of utility maximization if and only if it is the BI outcome. Both BS's formulation, and their proof, are complex and deep. We show that the result continues to hold when utility maximization is replaced by a rationality condition that is even more compelling; more important, the formulation and proof become far more transparent, accessible, and self-contained.

Suggested Citation

  • Itai Arieli & Robert J. Aumann, 2013. "The Logic of Backward Induction," Discussion Paper Series dp652, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp652
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    References listed on IDEAS

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    1. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
    2. Perea, Andrés, 2008. "Minimal belief revision leads to backward induction," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 1-26, July.
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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. Rich, Patricia, 2015. "Rethinking common belief, revision, and backward induction," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 102-114.
    4. Yannai A. Gonczarowski & Scott Duke Kominers & Ran I. Shorrer, 2019. "To Infinity and Beyond: A General Framework for Scaling Economic Theories," Papers 1906.10333, arXiv.org, revised Apr 2023.
    5. Asheim, Geir B. & Brunnschweiler, Thomas, 2023. "Epistemic foundation of the backward induction paradox," Games and Economic Behavior, Elsevier, vol. 141(C), pages 503-514.
    6. Vincent Mak & Darryl A. Seale & Eyran J. Gisches & Amnon Rapoport & Meng Cheng & Myounghee Moon & Rui Yang, 2018. "A network ridesharing experiment with sequential choice of transportation mode," Theory and Decision, Springer, vol. 85(3), pages 407-433, October.
    7. Franke, Marcel, 2021. "Eine Verhandlung zur Selektion der konstitutionenökonomischen Lösung," The Constitutional Economics Network Working Papers 03-2021, University of Freiburg, Department of Economic Policy and Constitutional Economic Theory.
    8. Balkenborg, Dieter, 2018. "Rationalizability and logical inference," Games and Economic Behavior, Elsevier, vol. 110(C), pages 248-257.
    9. Salvador Barberà & Anke Gerber, 2022. "Deciding On What To Decide," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 37-61, February.
    10. Salvador Barberà & Anke Gerber, 2017. "Deciding on what to Decide," Working Papers 973, Barcelona School of Economics.
    11. Joseph Y. Halpern & Yoram Moses, 2017. "Characterizing solution concepts in terms of common knowledge of rationality," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 457-473, May.

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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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