Informativeness and Trust in Bayesian Persuasion
Reema Deori, Ankur A. Kulkarni
TL;DR
The paper studies Bayesian persuasion with a sender who leverages private information to influence a receiver, introducing trust constraints that require signals to contain more truth than untruth. It shows that the Stackelberg game value (SGV) is exactly the optimum of a linear program $ extbf{P}(\\mathscr{U})$ over distributions $\\mu(\\hat x|x)$ satisfying the trust condition $\\mu(\\hat x|\\hat x) \\\ge \\\mu(\\hat x|x)$, and that informativeness $\\frak I(\\mathscr{U})$ is the optimum of a separate LP $\\textbf{I}(\\mathscr{U})$ capturing the minimum truthful revelation in any accumulation point of $\\varepsilon$-Stackelberg equilibria. The authors also provide closed-form SGV and informativeness for structured utility graphs (stars, chains, cycles) via a graph-theoretic obfuscation framework, and connect these results to prior deterministic-strategy findings. The work highlights that truthful disclosure is essential for persuasion to be effective and clarifies how information content and strategic payoff align under randomized signaling. Overall, the paper advances a tractable, information-theoretic view of persuasion where trust constraints tightly bound obfuscation and quantify inevitable truth revelation.
Abstract
A persuasion policy successfully persuades an agent to pick a particular action only if the information is designed in a manner that convinces the agent that it is in their best interest to pick that action. Thus, it is natural to ask, what makes the agent trust the persuader's suggestion? We study a Bayesian persuasion interaction between a sender and a receiver where the sender has access to private information and the receiver attempts to recover this information from messages sent by the sender. The sender crafts these messages in an attempt to maximize its utility which depends on the source symbol and the symbol recovered by the receiver. Our goal is to characterize the \textit{Stackelberg game value}, and the amount of true information revealed by the sender during persuasion. We find that the SGV is given by the optimal value of a \textit{linear program} on probability distributions constrained by certain \textit{trust constraints}. These constraints encode that any signal in a persuasion strategy must contain more truth than untruth and thus impose a fundamental bound on the extent of obfuscation a sender can perform. We define \textit{informativeness} of the sender as the minimum expected number of symbols truthfully revealed by the sender in any accumulation point of a sequence of $\varepsilon$-equilibrium persuasion strategies, and show that it is given by another linear program. Informativeness is a fundamental bound on the amount of information the sender must reveal to persuade a receiver. Closed form expressions for the SGV and the informativeness are presented for structured utility functions. This work generalizes our previous work where the sender and the receiver were constrained to play only deterministic strategies and a similar notion of informativeness was characterized. Comparisons between the previous and current notions are discussed.