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The logic of backward induction

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  • Arieli, Itai
  • Aumann, Robert J.

Abstract

Call a perfect information (PI) game simple if each player moves just once. Call a player rational if he never takes an action while believing, with probability 1, that a different action would yield him a higher payoff. Using syntactic logic, we show that an outcome of a simple PI game is consistent with common strong belief of rationality iff it is a backward induction outcome. The result also applies to general PI games in which a player's agents act independently, rendering forward inferences invalid.

Suggested Citation

  • Arieli, Itai & Aumann, Robert J., 2015. "The logic of backward induction," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 443-464.
    • Handle: RePEc:eee:jetheo:v:159:y:2015:i:pa:p:443-464
    DOI: 10.1016/j.jet.2015.07.004
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    References listed on IDEAS

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    Cited by:

    1. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    2. Asheim, Geir B. & Brunnschweiler, Thomas, 2023. "Epistemic foundation of the backward induction paradox," Games and Economic Behavior, Elsevier, vol. 141(C), pages 503-514.
    3. 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.
    4. 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.
    5. Rich, Patricia, 2015. "Rethinking common belief, revision, and backward induction," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 102-114.
    6. 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.
    7. 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.
    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

    Keywords

    Backward induction; Common strong belief; Perfect information; Syntactic interactive epistemology; Strong belief;
    All these keywords.

    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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