An Opinion Dynamics Model with Increasing Self-Confidence

TL;DR

This paper introduces a novel opinion dynamics model where agents increase their self-confidence over time, demonstrating convergence properties and connections to various social learning frameworks.

Contribution

The paper presents a new opinion dynamics model with increasing self-confidence and provides rigorous convergence analysis under different network conditions.

Findings

Proves convergence with a true opinion under fixed and periodic networks.

Establishes convergence bounds related to spectral gap and degree centrality.

Shows almost-sure convergence in randomly generated social networks.

Abstract

We propose an opinion dynamics model in which agents gradually increase their own self-confidence while interacting with each other. The relations between the newly proposed model and existing works of social learning, inertial opinion dynamics, Bayesian inference, and stochastic multi-armed bandits are demonstrated. We prove the convergence of the system with the existence of a truth under fixed and periodically changing social networks, and obtain tight convergence bounds related to the spectral gap of the graph Laplacian and the maximum total degree centrality, respectively. In the case of randomly generated social networks, an almost-sure convergence result is obtained. The dynamics of the model with multiple truths or zero truth is also discussed.