We develop a logical system that captures two different
interpretations of what extensive games model, and we apply this to a
long-standing debate in game theory between those who defend the
claim that common knowledge of rationality leads to backward
induction or subgame perfect (Nash) equilibria and those who reject
this claim. We show that a defense of the claim à la Aumann
(1995) rests on a conception of extensive game playing as a one-shot
event in combination with a principle of rationality that is
incompatible with it, while a rejection of the claim à la
Reny (1988) assumes a temporally extended, many-moment
interpretation of extensive games in combination with implausible
belief revision policies. In addition, the logical system provides
an original inductive and implicit axiomatization of rationality in
extensive games based on relations of dominance rather than the
usual direct axiomatization of rationality as maximization of
expected utility