From Common Knowledge of Rationality to Backward Induction

Abstract

With the only assumption that a player knows the strategy he chooses, it is proved in a generalized version of Aumann's (1995) epistemic model that, in a generic game with perfect information, common knowledge of rationality is equivalent to common knowledge of the fact that the backward induction strategy profile is chosen. This result shows that Aumann's backward induction theorem holds without stipulating partition knowledge structures nor presuming that the epistemic operator defines knowledge in the strict sense.