Bayesian Dissuasion with Bandit Exploration

Abstract

We investigate a two-period Bayesian persuasion game, where the receiver faces a decision, akin to a one-armed bandit problem: to undertake an action, gaining noisy information and a corresponding positive or negative payoff, or to refrain. The sender's objective is to dissuade the receiver from taking action by furnishing information about the payoff. Our findings describe the optimal strategy for the amount and timing of information disclosure. In scenarios where the sender possesses knowledge of the receiver's first-period action or observes a noisy public signal correlated with it, the optimal strategy entails revealing information in the second period. If this alone proves to be insufficient to dissuade the receiver from acting, supplementary information is provided in the first period. In scenarios where information must be provided without conditioning on the receiver's first-period action, the optimal strategy entails revealing information exclusively in the first period.

Figures (4)

• Figure 1: Receiver's optimal payoff (black) and sender's cost (red).
• Figure 2: The graphs of $q$ (red) and $\pi(q)$ (black), together with the sender's cost in equilibrium when $q>p^*$ (blue, dashed).
• Figure 3: Optimal splitting with Action-Based (dashed blue line), Signal-Based (dashed red line) or Unconditional Information (dashed black line)
• Figure A.1: Sender's payoff in the proof of Theorem \ref{['theorem:signal-based']}, with kink points at $q^{i}$ and $q^{ii}$.

Theorems & Definitions (8)

• Proposition 1: No Information Provision
• Proposition 2: Unconditional Information Provision
• Lemma 1
• Theorem 1: Action-Based Information Provision
• Theorem 2: Signal-Based Information Provision
• Definition : Extreme strategy
• Lemma 2
• proof