  We characterize three interrelated concepts in epistemic game theory:
permissibility, proper rationalizability, and iterated admissibility. We define
the lexicographic epistemic model for a game with incomplete information. Based
on it, we give two groups of characterizations. The first group characterizes
permissibility and proper rationalizability. The second group characterizes
permissibility in an alternative way and iterated admissibility. In each group,
the conditions for the latter are stronger than those for the former, which
corresponds to the fact that proper rationalizability and iterated
admissibility are two (compatible) refinements of permissibility within the
complete information framework. The intrinsic difference between the two groups
are the role of rationality: the first group does not need it, while the second
group does.
