Invariance and hierarchy-equivalence

TL;DR

This paper demonstrates that the behavioral implications of cautious rationality and common cautious belief are invariant across hierarchy-equivalent type structures, highlighting a fundamental robustness in belief hierarchy analysis.

Contribution

It establishes that hierarchy-equivalence of type structures preserves the behavioral implications of certain rationality and belief assumptions.

Findings

Behavioral implications are invariant across hierarchy-equivalent structures

Hierarchy-equivalence preserves belief hierarchy properties

Cautious rationality implications do not depend on specific type structures

Abstract

Two type structures are hierarchy-equivalent if they induce the same set of hierarchies of beliefs. This note shows that the behavioral implications of "cautious rationality and common cautious belief in cautious rationality" (Catonini and De Vito 2021) do not vary across hierarchy-equivalent type structures.