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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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    Cited by:

    1. Rich, Patricia, 2015. "Rethinking common belief, revision, and backward induction," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 102-114.
    2. repec:spr:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0535-9 is not listed on IDEAS

    More about this item

    Keywords

    Backward induction; Common strong belief; Perfect information; Syntactic interactive epistemology; Strong belief;

    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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