Behavioural versus Habitual Rationality and Backward Induction

The problem of finding sufficient conditions for backward induction in games of perfect information is analysed in a syntactic framework with subjunctive conditionals. The structure of the game is described by a logical formula. Two different rationality conditions are formulated, which are called behavioural and habitual rationality. While common knowledge of the former and the structure of the game does not imply backward induction, higher level knowledge of the latter and the structure of the game does. It is shown that similar results can be proven with non-introspective belief instead of knowledge.