Message-Enhanced DeGroot Model
Huisheng Wang, Zhanjiang Chen, H. Vicky Zhao
TL;DR
The paper tackles how dynamically evolving messages shape opinion formation on social networks by introducing a quantitative framework. It develops the Bounded Brownian Message (BBM) model to capture temporal continuity, randomness, and polarization of messages, and couples it with the DeGroot dynamics to form the Message-Enhanced DeGroot (MED) model. The authors derive the distribution and moments of BBM messages and characterize the mean and asymptotic variance of agents' opinions under MED, showing that the message mean tends to $\mu$ and the opinion mean likewise converges to $\mu$ with variance governed by $\mu(1-\mu)$ and network structure. Simulations validate the theoretical results, illustrating how external messages steer opinion evolution and how message variability propagates through the network, with implications for understanding and guiding opinion dynamics in message-rich environments.
Abstract
Understanding the impact of messages on agents' opinions over social networks is important. However, to our best knowledge, there has been limited quantitative investigation into this phenomenon in the prior works. To address this gap, this paper proposes the Message-Enhanced DeGroot model. The Bounded Brownian Message model provides a quantitative description of the message evolution, jointly considering temporal continuity, randomness, and polarization from mass media theory. The Message-Enhanced DeGroot model, combining the Bounded Brownian Message model with the traditional DeGroot model, quantitatively describes the evolution of agents' opinions under the influence of messages. We theoretically study the probability distribution and statistics of the messages and agents' opinions and quantitatively analyze the impact of messages on opinions. We also conduct simulations to validate our analyses.