Deductive reasoning in extensive games

We justify the application to extensive games of the concept of ‘fully permissible sets’, which corresponds to choice sets when there is common certain belief of the event that each player prefer one strategy to another if and only if the former weakly dominates the latter on the set of all opponent strategies or on the union of the choice sets that are deemed possible for the opponent. The extensive games considered illustrate how our concept yields support to forward induction, without necessarily promoting backward induction.