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Belief inducibility and informativeness.

P Jean-Jacques Herings1, Dominik Karos2, Toygar T Kerman3

  • 1Department of Econometrics and Operations Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands.

Theory and Decision
|May 16, 2024
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Summary
This summary is machine-generated.

This study analyzes how sender signals influence receiver beliefs in a world with private, correlated messages. It reveals that any belief distribution can be achieved using language-independent signals, with minimal signals offering the least information.

Keywords:
Game theoryInducible distributionsInformation designInformativeness

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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.