TR-2010010: Robust Knowledge and Rationality

In 1995, Aumann proved that in games of perfect information, common knowledge of rationality yields backward induction. In 1998, Stalnaker provided an example of a game in which common knowledge of rationality, once belief revision is taken into account, does not yield backward induction. However, in some pertinent situations in this example, players are allowed to forfeit the rationality condition. We introduce the notion of robust knowledge which extends common knowledge to all relevant situations, including counterfactual ones. Robust knowledge of rationality, in a general belief revision setting, represents the “no irrationality in the system” condition which is at the heart of the backward induction argument. We show that in games of perfect information, robust knowledge of rationality yields backward induction. This may be regarded as a natural form of Aumann’s theorem which accommodates belief revision.