On the Convergence of an Opinion-Action Coevolution Model with Bounded Confidence

TL;DR

This paper provides a theoretical analysis of an opinion-action coevolution model with bounded confidence, showing conditions for convergence to consensus or clustering, supported by numerical simulations.

Contribution

It introduces a reformulation of the model into an augmented state-space and derives convergence conditions based on existing theoretical frameworks.

Findings

Model converges to consensus if the interaction digraph stabilizes.

Model exhibits clustering with stationary leaders under certain conditions.

Numerical simulations validate the theoretical convergence results.

Abstract

This paper presents a theoretical convergence analysis for an opinion-action coevolution model that integrates the opinion updating rule of the Hegselmann-Krause model with a utility-based decision-making mechanism. The model is reformulated into an augmented state-space representation, where the state matrix induces a time-varying social interaction digraph. The convergence analysis is grounded on two existing theoretical findings that establish convergence for the Hegselmann-Krause type of models and containment control systems with multiple stationary leaders, respectively. Results indicate that, if the structure of the interaction digraph stabilizes within finite time, the model either converges to consensus, where all agents' opinions and actions reach an identical state, or exhibits clustering, where some opinion nodes act as stationary leaders while the remaining nodes approach the convex hull formed by the leaders. Numerical simulations are then provided to validate the theoretical results.