Abstract Backward induction is characterized in an epistemic model of perfect information games where players have common certain belief of the consistency of preferences rather than the rationality of choice. In this approach, backward induction corresponds to common certain belief of ‘belief in each subgame of opponent rationality’. At an interpretative level this result resembles the one established by Aumann [Games Econ. Behav. 8 (1995) 6–19]. By instead imposing common certain belief of ‘belief ( only in the whole game) of opponent rationality’, Ben-Porath’s [Rev. Econ. Stud. 64 (1997) 23–46] support for the Dekel–Fudenberg procedure is interpreted.