Timely Information for Strategic Persuasion

2025-12-04

AI Summary

This paper studies how a strategic sender, under resource constraints, can dynamically control the timing of information disclosure to induce the receiver to overestimate the state as 1—regardless of its true value—while the receiver seeks accurate estimation. Method: Building on the Bayesian persuasion framework, we model state evolution via a continuous-time Markov chain (CTMC) and formulate the sequential interaction as a dynamic game with incentive compatibility (IC) constraints, solved via dynamic programming. Contribution/Results: We introduce “information timeliness steering”—a novel paradigm wherein the sender optimally concentrates limited sampling resources on state 1 and minimizes observation frequency of unfavorable states. We prove that this strategy strictly satisfies the receiver’s rationality constraint and significantly enhances long-term persuasion efficacy: it maximizes the time proportion during which the receiver estimates the state as 1, both in single- and multi-source settings.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Reasoning under Uncertainty: Sequential Decision Making
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

This work investigates a dynamic variant of Bayesian persuasion, in which a strategic sender seeks to influence a receiver's belief over time through controlling the timing of the information disclosure, under resource constraints. We consider a binary information source (i.e., taking values 0 or 1), where the source's state evolve according to a continuous-time Markov chain (CTMC). In this setting, the receiver aims to estimate the source's state as accurately as possible. In contrast, the sender seeks to persuade the receiver to estimate the state to be 1, regardless of whether this estimate reflects the true state. This misalignment between their objectives naturally leads to a Stackelberg game formulation where the sender, acting as the leader, chooses an information-revelation policy, and the receiver, as the follower, decides whether to follow the sender's messages. As a result, the sender's objective is to maximize the long-term average time that the receiver's estimate equals 1, subject to a total sampling constraint and a constraint for the receiver to follow the sender's messages called incentive compatibility (IC) constraint. We first consider the single-source problem and show that the sender's optimal policy is to allocate a minimal sampling rate to the undesired state 0 (just enough to satisfy the IC constraint) and assign the remaining sampling rate to the desired state 1. Next, we extend the analysis to the multi-source case, where each source has a different minimal sampling rate. Our results show that the sender can leverage the timeliness of the revealed information to influence the receiver, thereby achieving a higher utility.

Problem

• Dynamic Bayesian persuasion with resource constraints on information timing.
• Misaligned sender-receiver objectives modeled as a Stackelberg game.
• Optimal policy maximizes receiver's estimate of state 1 under constraints.

Innovation

• Sender controls information timing via continuous-time Markov chain
• Optimal policy allocates minimal sampling to undesired states
• Leverages timeliness to influence receiver under incentive constraints