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Title:A dynamic epistemic characterization of backward induction without counterfactuals PDF Logo
Authors:Bonanno, Giacomo
Issue Date:2012
Series/Report no.:Working Papers, University of California, Department of Economics 12,2
Abstract:The analysis of rational play in dynamic games is usually done within a static framework that specifies a player's initial beliefs as well as his disposition to revise those beliefs conditional on hypothetical states of information. We suggest a simpler approach, where the rationality of a player's choice is judged on the basis of the actual beliefs that the player has at the time he has to make that choice. We propose a dynamic framework where the set of possible worlds is given by state-instant pairs (w,t). Each state w specifies the entire play of the game and, for every instant t, (w,t) specifies the history that is reached at that instant (in state w). A player is said to be active at (w,t) if the history reached in state w at date t is a decision history of his. At every state-instant pair (w,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 said to be rational at (w,t) if either he is not active there or the action he ends up taking at state w is optimal given his beliefs at (w,t). We provide a characterization of 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. Thus our epistemic characterization does not rely on dispositional belief revision or on (objective or subjective) counterfactuals.
Subjects:perfect-information game
backward induction
dynamic interactive beliefs
rationality
Kripke frame
Document Type:Working Paper
Appears in Collections:Working Papers, Department of Economics, UC Davis

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