Details

Autor(en) / Beteiligte

• Bonanno, Giacomo

Titel

A dynamic epistemic characterization of backward induction without counterfactuals

Ist Teil von

• Games and economic behavior, 2013-03, Vol.78, p.31-43

Ort / Verlag

Duluth: Elsevier Inc

Erscheinungsjahr

2013

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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. ► Rationality is judged on the basis of the actual beliefs that the player has at the time of choice. ► Possible worlds are state-instant pairs (ω,t). Each state specifies the entire play of the game. ► A playerʼs beliefs provide an answer to: “What will happen if I take action a?”, for every action a. ► A player is rational at (ω,t) if the action he ends up taking at ω is optimal given his beliefs at (ω,t). ► We provide a characterization of backward induction that does not rely on counterfactuals.