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A dynamic epistemic characterization of backward induction without counterfactuals

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  • Bonanno, Giacomo

Abstract

We propose a dynamic framework where the rationality of a playerʼs choice is judged on the basis of the actual beliefs that he has at the time he makes that choice. The set of “possible worlds” is given by state-instant pairs (ω,t), where each state specifies the entire play of the game. At every (ω,t) the beliefs of the active player provide an answer to the question “what will happen if I take action a?”, for every available action a. A player is rational at (ω,t) if either he is not active or the action he takes is optimal given his beliefs. We characterize backward induction in terms of the following event: the first mover (i) is rational and has correct beliefs, (ii) believes that the active player at date 1 is rational and has correct beliefs, (iii) believes that the active player at date 1 believes that the active player at date 2 is rational and has correct beliefs, etc.

Suggested Citation

  • Bonanno, Giacomo, 2013. "A dynamic epistemic characterization of backward induction without counterfactuals," Games and Economic Behavior, Elsevier, vol. 78(C), pages 31-43.
  • Handle: RePEc:eee:gamebe:v:78:y:2013:i:c:p:31-43
    DOI: 10.1016/j.geb.2012.12.004
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 1111, University of California, Davis, Department of Economics.
    2. Giacomo Bonanno & Cédric Dégremont, 2013. "Logic and Game Theory," Working Papers 135, University of California, Davis, Department of Economics.
    3. Bonanno, Giacomo, 2014. "A doxastic behavioral characterization of generalized backward induction," Games and Economic Behavior, Elsevier, vol. 88(C), pages 221-241.
    4. Zuazo-Garin, Peio, 2017. "Uncertain information structures and backward induction," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 135-151.

    More about this item

    Keywords

    Perfect-information game; Backward induction; Dynamic interactive beliefs; Rationality; Kripke frame;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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