A dynamic epistemic characterization of backward induction without counterfactuals

► 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.