Belief inducibility and informativeness

Area of Science:

• Decision Theory
• Information Economics
• Game Theory

Background:

• Receivers share a common prior belief over a finite state space.
• Receivers observe private, correlated messages contingent on the true state.
• The study focuses on beliefs induced by sender-chosen signals.

Purpose of the Study:

• To comprehensively analyze the inducible distributions of posterior beliefs.
• To classify signals (minimal, individually minimal, language-independent) and their impact on information revelation.
• To determine the characteristics of the least informative signals for inducing fixed belief distributions.

Main Methods:

• Classification of signals based on their properties (minimal, individually minimal, language-independent).
• Analysis of the set of all inducible distributions of posterior beliefs.
• Investigation of higher-order information revealed by different signal classes.

Main Results:

• Any inducible distribution of posterior beliefs can be induced by a language-independent signal.
• Language-independent signals are sufficient for generating all possible inducible belief distributions.
• The least informative signals for a fixed belief distribution are found within the relative interior of language-independent signals.

Conclusions:

• The study provides a framework for understanding belief formation under strategic signaling.
• Language-independent signals play a crucial role in determining the space of possible receiver beliefs.
• Characterizing minimal signals helps understand the boundary of information transmission in such settings.