Competitive resource allocation on a network considering opinion dynamics with self-confidence evolution

The formation of public opinion is typically influenced by different stakeholders, such as governments and firms. Recently, various real-world problems related to the management of public opinion have emerged, necessitating stakeholders to strategically allocate resources on networks to achieve their objectives. To address this, it is imperative to consider the dynamics of opinion formation. Notably, in existing opinion dynamics models, individuals possess self-confidence parameters reflecting their adherence to historical opinions. However, most extant studies assume the individuals’ self-confidence levels remain constant over time, which cannot accurately capture the intricacies of human behavior. In response to this gap, we first introduce a self-confidence evolution model, which encompasses two influencing factors: the self-confidence levels of one's group mates and the passage of time. Furthermore, we present the social network DeGroot model with self-confidence evolution, and conduct some theoretical analyses. Moreover, we propose a game model to identify the optimal resource allocation strategies of players on a network. Finally, we provide sensitivity analyses, comparative studies, and a case study. This paper highlights the significance of incorporating self-confidence evolution into the process of opinion dynamics, and the results can provide valuable practical insights for players seeking to improve their optimal resource allocation on a network to more effectively manage public opinions.