TR-2010007: Robust Knowledge of Rationality

Stalnaker provided an example of a perfect information game in which common knowledge of rationality does not yield backward induction. However, in his example, knowledge is treated as defeasible: players forfeit their knowledge of rationality at some vertices. This is not how ‘knowledge’ is understood in epistemology where, unlike belief, it is not subject to revision. In this respect, the Stalnaker example is a fit for ‘rationality and common belief of rationality’ rather than ‘common knowledge of rationality.’ In order to represent knowledge in the belief revision setting we introduce the notion of ‘robust knowledge’ which is maintained whenever possible during belief revision. We show that robust knowledge of Stalnaker rationality in games of perfect information yields backward induction.