Characterizing Permissibility, Proper Rationalizability, and Iterated Admissibility by Incomplete Information

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.