A dynamic epistemic characterization of backward induction without counterfactuals
AbstractWe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Games and Economic Behavior.
Volume (Year): 78 (2013)
Issue (Month): C ()
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Web page: http://www.elsevier.com/locate/inca/622836
Perfect-information game; Backward induction; Dynamic interactive beliefs; Rationality; Kripke frame;
Other versions of this item:
- Giacomo Bonanno, 2012. "A dynamic epistemic characterization of backward induction without counterfactuals," Working Papers 122, University of California, Davis, Department of Economics.
- C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
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