2 research outputs found
Ordered Kripke Model, Permissibility, and Convergence of Probabilistic Kripke Model
We define a modification of the standard Kripke model, called the ordered
Kripke model, by introducing a linear order on the set of accessible states of
each state. We first show this model can be used to describe the lexicographic
belief hierarchy in epistemic game theory, and perfect rationalizability can be
characterized within this model. Then we show that each ordered Kripke model is
the limit of a sequence of standard probabilistic Kripke models with a modified
(common) belief operator, in the senses of structure and the
(epsilon-)permissibilities characterized within them
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.Comment: arXiv admin note: substantial text overlap with arXiv:1801.0471