Cautious belief and iterated admissibility

We define notions of cautiousness and cautious belief to provide epistemic conditions for iterated admissibility in finite games. We show that iterated admissibility characterizes the behavioral implications of "cautious rationality and common cautious belief in cautious rationality"in a terminal lexicographic type structure. For arbitrary type structures, the behavioral implications of these epistemic assumptions are characterized by the solution concept of self-admissible set (Brandenburger et al., 2008). We also show that analogous results hold under alternative epistemic assumptions, in particular if cautiousness is "transparent"to the players.