Strategic Persuasion Through Information Timeliness

2026-07-17

AI Summary

This study addresses how a sender can achieve effective persuasion by strategically controlling the timing of truthful information updates when their objective conflicts with that of a receiver. The authors formulate a continuous-time Stackelberg game in which the sender sets state-dependent Poisson update rates, while the receiver decides whether to adopt the information, subject to participation constraints and an intensity budget. The sender aims to maximize the fraction of time the state is estimated as 1. Theoretical analysis reveals that optimal persuasion can be attained solely through managing information timeliness: in the single-source case, the minimal necessary update intensity is allocated to the undesired state 0 to satisfy constraints, with all remaining budget devoted to state 1. Furthermore, the paper proposes an efficient branch-and-bound algorithm that enables scalable computation for heterogeneous multi-source and multi-receiver settings without exhaustive search.

Abstract

We study a dynamic strategic communication problem in which a sender controls the timing of truthful updates from binary continuous-time Markov sources. The receiver chooses between a zero-order-hold estimator that follows the sender's updates and a prior-only default estimator, aiming to maximize a weighted correct-estimation utility. In contrast, the sender seeks to persuade the receiver to estimate the state as 1, regardless of the true state. This misalignment leads to a Stackelberg game in which the sender, as the leader, commits to state-dependent Poisson update rates, and the receiver, as the follower, decides whether to follow the sender's messages. The sender maximizes the long-term average time that the receiver's estimate equals 1, subject to a conditional intensity budget and a participation constraint (PC) ensuring that following the sender's messages does not degrade the receiver's average utility relative to its prior information. For a single source, we show that the sender's optimal policy allocates a minimum state-0 update intensity to the undesired state-0, just enough to satisfy the PC, and the remaining budget to the desired state-1. For multiple sources with heterogeneous minimum state-0 update intensities, we develop a branch-and-bound algorithm that typically avoids exhaustive search. Finally, we extend the solution to multiple receivers over dedicated channels. Our results show that controlling timeliness alone enables the sender to persuade the receiver and increase its utility.

Problem

• strategic persuasion
• information timeliness
• Stackelberg game
• participation constraint
• Poisson update rates

Innovation

• strategic communication
• information timeliness
• Stackelberg game
• Poisson update rate
• branch-and-bound algorithm