Ordered Kripke Model, Permissibility, and Convergence of Probabilistic Kripke Model

TL;DR

This paper introduces the ordered Kripke model, a new framework that captures lexicographic belief hierarchies and rationalizability, and demonstrates its convergence from probabilistic models.

Contribution

It defines the ordered Kripke model, linking it to belief hierarchies and rationalizability, and proves its approximation by probabilistic Kripke models.

Findings

Ordered Kripke models describe lexicographic belief hierarchies.

Perfect rationalizability characterized within ordered Kripke models.

Ordered models are limits of probabilistic Kripke models.

Abstract

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.