Arnis Vilks

• We analyse the epistemic conditions for the backwards induction play in games of perfect information. Unlike most previous literature on the subject, we explicitly pay attention to players’ knowledge of the game, avoid counterfactuals, and use the syntactic approach of epistemic logic. Conditions of rationality are formulated in terms of moves (instead of strategies), and various assumptions on the feasibility of moves are considered. The main result says that the backwards induction play is implied by sufficiently high order mutual knowledge of (1) the structure of the game, (2) material rationality, and (3) subjective feasibility of all moves which belong to the backwards induction profile. The order of mutual knowledge is sufficiently high, if it is of the length of the game minus one. The main question raised by our analysis is this: What does the assumption that a particular game will be played imply about the feasibility of its moves?