Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Delegated Information Provision

Francesco Bilotta, Christoph Carnehl, Justus Preusser

Abstract

A designer relies on an experimenter to provide information to a decision maker, but the experimenter has incentives to persuade rather than merely transmit information. Anticipating this motive, the designer can restrict the set of admissible experiments, but cannot prevent the experimenter from garbling any admissible experiment. We model this situation as delegation over experiments. The optimal delegation set can be obtained by comparing maximally informative experiments among those the experimenter has no incentive to garble. When the experimenter's preferences are $S$-shaped, we fully characterize such experiments as double censorship. Relative to the full delegation outcome, upper censorship, double censorship features an intermediate pooling region, inducing a smaller pooling region for the highest states. We show that the designer strictly benefits from imposing a nontrivial delegation set to constrain the experimenter's ability to persuade while retaining valuable information provision.

Delegated Information Provision

Abstract

A designer relies on an experimenter to provide information to a decision maker, but the experimenter has incentives to persuade rather than merely transmit information. Anticipating this motive, the designer can restrict the set of admissible experiments, but cannot prevent the experimenter from garbling any admissible experiment. We model this situation as delegation over experiments. The optimal delegation set can be obtained by comparing maximally informative experiments among those the experimenter has no incentive to garble. When the experimenter's preferences are -shaped, we fully characterize such experiments as double censorship. Relative to the full delegation outcome, upper censorship, double censorship features an intermediate pooling region, inducing a smaller pooling region for the highest states. We show that the designer strictly benefits from imposing a nontrivial delegation set to constrain the experimenter's ability to persuade while retaining valuable information provision.
Paper Structure (45 sections, 15 theorems, 48 equations, 8 figures)

This paper contains 45 sections, 15 theorems, 48 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Model
  3. Examples of Restrictions
  4. Restrictions on communication.
  5. Restrictions on measurement.
  6. Attention management.
  7. Privacy-preserving signals.
  8. Benchmark: Full Delegation
  9. Maximal Incentive-Compatible Experiments
  10. Motivation and Definition
  11. Double Censorship
  12. Characterization
  13. Sketch of the Proof
  14. Optimal Delegation
  15. Full delegation is not optimal
  16. ...and 30 more sections

Key Result

Proposition 1

There is a unique best reply $F^\ast$ to $H$. In particular, $F^\ast$ is an upper censorship experiment with a threshold $x^\ast$ and an atom $y^\ast = \mathbb{E}_H[\bm{\omega} \mid \bm{\omega} \geq x^{\ast}]$ satisfying $0 < x^{\ast} < r_{0} < y^{\ast}< 1$ and

Figures (8)

  • Figure 1: The ICDFs of the prior $H$, the degenerate experiment $\delta_{\mu}$, and an experiment $F$ that pools $H$ above a threshold $x$ to a point $y$, and else coincides with $H$.
  • Figure 2: \ref{['eq:unrestricted_persuasion_FOC']} defines the optimal upper censorship experiment, illustrated by the red dotted line. The tangent to $G$ at $y^{\ast}$ intersects $G$ at $x^{\ast}$. Since $x^{\ast} < r_{0}$, some states in the convex region of the experimenter's payoff are also pooled into the high atom $y^{\ast}$.
  • Figure 3: The ICDF of double censorship $F$ with thresholds $(s, t)$ and atoms $(x, y)$.
  • Figure 4: The order of the set $P$. For a higher value of $y$, the slope of $y$ is lower, meaning the tangent to $G$ at $y$ intersects $G$ below $r_{0}$ at a lower point $x$.
  • Figure 5: Characterization of MIC experiments. For readability, the horizontal axes are truncated at the top.
  • ...and 3 more figures

Theorems & Definitions (30)

  • Definition 1
  • Definition 2
  • Proposition 1: kolotilin2022censorship
  • Definition 3
  • Lemma 1
  • Remark
  • Definition 4
  • Theorem 1
  • Corollary 1
  • Lemma 2
  • ...and 20 more