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.

中文翻译：

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通过不完整信息表征可容许性、适当合理化和迭代可容许性

我们描述了认知博弈论中三个相互关联的概念：可容许性、适当合理化和迭代可容许性。我们为具有不完整信息的游戏定义了词典认知模型。在此基础上，我们给出了两组表征。第一组描述了可允许性和适当的合理性。第二组以另一种方式描述可容许性和迭代可容许性。在每一组中，后者的条件强于前者，这对应于适当的合理化和迭代的可容许性是完整信息框架内的两个（兼容的）可容许性细化的事实。两组之间的内在区别在于理性的作用：第一组不需要它，而第二组需要。