Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Persuasion with Ambiguous Communication

Xiaoyu Cheng, Peter Klibanoff, Sujoy Mukerji, Ludovic Renou

Abstract

We explore whether ambiguous communication can be beneficial to the sender in a persuasion problem, when the receiver (and possibly the sender) is ambiguity averse. Our analysis highlights the necessity of using a collection of experiments that form a splitting of an obedient experiment. Some experiments in the collection must be Pareto-ranked in that both players agree on their payoff ranking. If an optimal Bayesian persuasion experiment can be split in this way, then any not-too-ambiguity-averse sender as well as the receiver benefit. There are no benefits when the receiver has only two actions.

Persuasion with Ambiguous Communication

Abstract

We explore whether ambiguous communication can be beneficial to the sender in a persuasion problem, when the receiver (and possibly the sender) is ambiguity averse. Our analysis highlights the necessity of using a collection of experiments that form a splitting of an obedient experiment. Some experiments in the collection must be Pareto-ranked in that both players agree on their payoff ranking. If an optimal Bayesian persuasion experiment can be split in this way, then any not-too-ambiguity-averse sender as well as the receiver benefit. There are no benefits when the receiver has only two actions.
Paper Structure (29 sections, 32 theorems, 80 equations, 2 figures, 1 table)

This paper contains 29 sections, 32 theorems, 80 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. An Introductory Example
  3. Persuasion with Ambiguous Communication
  4. The Model
  5. A Revelation Principle
  6. Incentive Compatibility and Effective Measure
  7. Properties of Optimal Persuasion with Ambiguous Communication
  8. When Does Ambiguous Communication Benefit The Sender?
  9. Benefits from Binary Ambiguous Communication
  10. Further Discussion
  11. What if the sender knows the resolution of ambiguity in advance?
  12. Robustness to Small Misperceptions
  13. Robustness to Pre-Existing Ambiguity about Payoff-Relevant States
  14. Concavification
  15. Related Literature
  16. ...and 14 more sections

Key Result

Proposition 1

For any $((\boldsymbol{\sigma}, \mu), \tau)$ such that $\tau \in BR(\boldsymbol{\sigma}, \mu)$, there exists a canonical and obedient ambiguous experiment $(\boldsymbol{\sigma}^{*}, \mu)$ such that $u_{i}(\sigma_{\theta}, \tau) = u_{i}(\sigma^{*}_{\theta}, \tau^{*})$ for all $i \in \{s,r\}$ and $\th

Figures (2)

  • Figure 1: Sender's indirect utility (thick curve) and its concavification (thick dashed curve)
  • Figure 2: Construction of the ambiguous experiment

Theorems & Definitions (74)

  • Definition 1
  • Definition 2
  • Definition 3
  • Proposition 1
  • Definition 4
  • Lemma 1
  • Remark 1
  • Definition 5
  • Theorem 1
  • Proposition 2
  • ...and 64 more