On the Convergence of an Opinion-Action Coevolution Model with Bounded Confidence
This provides theoretical insights for modeling social systems where opinions and actions coevolve, but it is incremental as it builds on existing convergence results.
The paper analyzes the convergence behavior of an opinion-action coevolution model combining Hegselmann-Krause opinion dynamics with utility-based decision-making, showing that under stable interaction structures, the model converges to consensus or clustering with stationary leaders.
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.