Characterizing Assumption of Rationality by Incomplete Information

TL;DR

This paper explores how the assumption of rationality in two-player games can be characterized within incomplete information models, linking belief hierarchies across different informational frameworks.

Contribution

It provides a formal characterization of the common assumption of rationality using belief hierarchies in incomplete information settings, connecting it to complete information models.

Findings

Belief hierarchies in incomplete info models can express common rationality assumptions.

A belief hierarchy expresses common rationality iff it satisfies caution, rationality, support for good choices, and prior beliefs.

The characterization bridges complete and incomplete information frameworks for rationality assumptions.

Abstract

We characterize common assumption of rationality of 2-person games within an incomplete information framework. We use the lexicographic model with incomplete information and show that a belief hierarchy expresses common assumption of rationality within a complete information framework if and only if there is a belief hierarchy within the corresponding incomplete information framework that expresses common full belief in caution, rationality, every good choice is supported, and prior belief in the original utility functions.