Bayesian Persuasion

Motivated by modern marketplaces, where the platform or the seller routinely gathers detailed user profiles, we study a novel learning theoretic model that simultaneously involves information and mechanism design. Specifically, we consider the economic setting recently introduced by Bergemann et al. (2022), where in addition to the menu of quality-price pairs, the seller offers information on the value of the match between product quality and buyer's taste via a signaling scheme. We relax the assumption that the seller knows the buyers' belief about the distribution of tastes and study the sample requirements of designing a revenue maximizing scheme. We consider both the batch setting where we have access to data from a set of i.i.d. buyers and an online demand query model where we observe the buyers' behaviors to seller's schemes. Despite the apparent non-convexity of the problem, we also give the first FPTAS to compute a scheme that maximizes the revenue within an arbitrarily small additive loss, which was left open by Bergemann et al. (2022). Overall, this brings a new learning perspective in asymmetric economic settings where buyers and sellers know different types of information.

The paper examines the strategic behavior of Gen AI chatbots used for emotional support. Using a Bayesian Persuasion, we model interactions between chatbots that send signals about users' emotional states and users who decide whether to engage based on these signals. We demonstrate that chatbots face economic incentives to occasionally misrepresent users' emotional conditions to maximize engagement metrics. Our equilibrium analysis reveals that the optimal strategy for chatbots involves truthfully reporting when users genuinely need support, but strategically misreporting emotional need when users are in good emotional states. Interestingly, this deception increases chatbot engagement without reducing users' expected payoff. More skeptical users receive more honest assessments, as chatbots cannot afford to lie to users with higher engagement thresholds. While our model suggests that deception can occur without payoff reduction, it raises significant ethical and regulatory concerns.

Bayesian persuasion studies how an informed sender can influence the behavior of a receiver through strategic information disclosure. Standard models assume the sender is the receiver's only source of information, yet in many applications receivers also consult external sources the sender can neither observe nor control. We study an online Bayesian persuasion problem in which a binary-action receiver has access to a fixed signaling scheme that is unknown to the sender. Over $T$ rounds, the sender commits to a signaling scheme and sends a signal; the receiver combines it with its private signal and acts, while the sender observes only the action. We design a learning algorithm that achieves regret $\widetilde{O}(T^{3/4})$ relative to the optimal scheme of a sender who knows the private signaling scheme of the receiver, with polynomial dependence on the sizes of the state space and the receiver's signal alphabet. Our key insight is reducing the problem of learning the exponentially large belief-space partitioning induced by the private scheme to a one-dimensional change-point detection problem.

Interactive driving, wherein an intelligent lead vehicle equipped with real-time traffic data coordinates route choices of connected vehicles, offers a promising approach to dynamic traffic management. To address the challenge of harmonising decisions, this paper considers the strategic information revealing framework of Bayesian persuasion. Here, the principal (lead vehicle) aims to guide the agent's (connected vehicle) partially observable sequential decision making towards its own objectives by selectively revealing information, such as real-time traffic ahead, using signals. However, the agent's farsighted response to maximize its long-term reward, renders the principal's signaling strategy design computationally challenging. We propose an online structured reinforcement learning framework to synthesize computationally efficient signaling strategy which is persuasive for a far-sighted agent. The main contributions of the paper are as follows: (i) For a monotonic agent with approximate best response, we propose MAPL, a structured policy learning algorithm for faster online learning, (ii) Identification of sufficient conditions for the supermodular structure of the Q function of the principal for a monotonic agent, (iii) Identification of sufficient conditions to ensure the persuasiveness of the principal's signaling strategy, (iv) Supermodular Q learning for Principal (SQP), which leverages the supermodular structure of principal's action value to synthesize computationally efficient signaling strategy that is persuasive for a monotonic learning agent, (v) Numerical analysis considering a real-time application of Bayesian persuasive driving for lane selection demonstrates that the proposed method is 30% cost efficient for optimising travelling rewards of both the lead and connected vehicle compared to the existing methodologies for signaling strategy design.

Misalignment can change how information moves from an AI agent to a human user. We model this as an information advantage: the AI agent observes the world state, while the human receiver only knows a prior and must act after seeing the agent's signal. A strategic AI sender may withhold evidence or garble information in order to steer the human's decision. We ask how much useful information can still reach the human when the AI optimizes a misaligned objective. We study a Bayesian persuasion model in which the world state is a bit string, the human receiver wants to guess the bits correctly, and a single AI sender wants the receiver to guess as many bits as possible as $1$. For a prior $μ$, let $R_0(μ)$ be the receiver's utility from using only the prior, and let $R_{\max}(μ)$ be the largest receiver utility among signaling schemes that are optimal for the sender. We prove $R_{\max}(μ)/R_0(μ)\leq 3/2$. This bound improves for priors close to the independent product prior with the same marginals: if $μ(x)\geq (1-η)π_μ(x)$ for every state $x$, then $R_{\max}(μ)\leq R_0(μ)+ηn$. We also give a six-bit prior for which $R_{\max}(μ)/R_0(μ)=39/31>5/4$, so no universal $5/4$ bound is possible.

Mixed autonomy driving becomes unsafe and inefficient when autonomous vehicles (AVs) and human-driven vehicles (HVs) misread each other's intentions. We study this problem as implicit mutual communication in lane changes. The proposed framework models how the ego vehicle both expresses its intent and probes the other driver's preference under epistemic uncertainty. It combines a level-k Bayesian persuasion game with virtual features for proactive signaling, information-theoretic rewards for mutual communication, and adaptive weights of communication affordances. We further introduce the Pride-Inquiry (P-I) and Pride-Prejudice (P-P) planes to analyze communication intensity and tendency. The model is calibrated with a Communication-Based Multi-Agent Inverse Reinforcement Learning algorithm (C-MIRL) on the naturalistic NGSIM dataset. Compared with the non-communicative baseline, the proposed model reduces the prediction error of mandatory lane changes by up to 20% while maintaining strong generalization. Driver-In-the-Loop questionnaire scores are positively correlated with the calibrated communication variables, supporting the subjective validity of the model. The learned rewards further show that inquiry and listening affordances contribute more than pride and expression alone, and that inquiry preference varies more strongly across drivers. These results support explicit modeling of mutual communication and epistemic uncertainty in interactive driving.

Classical Bayesian persuasion studies how a sender influences receivers through carefully designed signaling policies within a single strategic interaction. In many real-world environments, such interactions are repeated across multiple games, creating opportunities to exploit structural similarity across tasks. In this work, we introduce Meta-Persuasion algorithms, establishing the first line of theoretical results for both full-feedback and bandit-feedback settings in the Online Bayesian Persuasion (OBP) and Markov Persuasion Process (MPP) frameworks. We show that our proposed meta-persuasion algorithms achieve provably sharper regret rates under natural notions of task similarity, improving upon the best-known convergence rates for both OBP and MPP. At the same time, they recover the standard single-game guarantees when the sequence of games is picked arbitrarily. Finally, we complement our theoretical analysis with numerical experiments that highlight our regret improvements and the benefits of meta-learning in repeated persuasion environments.

Large language models (LLMs) still struggle with strategic persuasion, largely because existing approaches either neglect information asymmetry or rely on unrealistic pre-commitment assumptions. We introduce a type-induced commitment-communication mechanism that grounds Bayesian Persuasion (BP) in natural language dialogue without pre-commitment: the persuader narrates their potential types (e.g., honest vs. dishonest) to dynamically construct an information schema, enabling the persuadee to perform Bayesian belief updates within the conversation itself. We implement two variants: Semi-Formal-Natural-Language (SFNL) and Fully-Natural-Language (FNL), evaluating them against strong baselines across multiple LLMs and human judges. BP strategies consistently outperform baselines: SFNL excels in logical credibility, while FNL shows superior robustness and emotional resonance. We verify that gains stem from genuine Bayesian reasoning rather than superficial formatting, and we further show that supervised fine-tuning enables small models to match the persuasive performance of much larger ones.