Scientific publications

In opinion dynamics, consensus formation is a dynamic and iterative process in which external players influence agents’ opinions through feedback-based decision mechanisms. In this paper, we study a dynamic game model of opinion evolution in a social network with average-based interactions, where a subset of agents exhibits stubborn behavior characterized by heterogeneous stubbornness parameters, while being influenced by external players. The players aim to steer the opinions of all agents toward a common desired value. The proposed model is formulated as a discrete-time linear–quadratic dynamic game. Using the Bellman equation, we derive the feedback Nash equilibrium strategies and the corresponding optimal opinion trajectories. Theoretical analysis characterizes the convergence behavior and identifies conditions under which opinion consensus is achieved. Numerical simulations illustrate how average-based interactions and the locations of stubborn agents affect consensus formation under different control strategies. In addition, the impact of unknown agent stubbornness on the players’ payoffs is investigated. The results provide insights into the interplay between network structure, agent stubbornness, and strategic control in guiding opinion consensus.