  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, Friedenberg and Keisler 2008).
We also show that analogous conclusions hold under alternative epistemic
assumptions, in particular if cautiousness is "transparent" to the players.
  KEYWORDS: Epistemic game theory, iterated admissibility, weak dominance,
lexicographic probability systems. JEL: C72.
