Template-Type: ReDIF-Paper 1.0
Author-Name: Giacomo Bonanno
Author-Name-First: Giacomo
Author-Name-Last: Bonanno
Author-Workplace-Name: Department of Economics, University of California Davis
Title: A dynamic epistemic characterization of backward induction without counterfactuals
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.
Length: 17
File-URL: https://repec.dss.ucdavis.edu/files/D1xbR5jboe81bfxNF5BsQdb1/12-2.pdf
File-Format: application/pdf
Number: 10
Classification-JEL: C7
KeyWords: Perfect-information game, backward induction, dynamic interactive beliefs, rationality, Kripke frame
Creation-Date: 20120317
Handle: RePEc:cda:wpaper:10