Promoting cooperation through dynamic trustworthiness in spatial public goods games

The established imitation protocol mandates that participants observe and learn strategies from the most successful individuals in their vicinity. Previous studies have highlighted the critical role of this protocol in understanding the mechanisms that drive the evolution of cooperation. Nevertheless, individuals often exhibit a natural reluctance to adopt substantial changes rapidly. In this context, we integrate the concept of investment trustworthiness into the strategy updating process and explore the outcomes of dynamic beliefs through numerical simulations. Our results demonstrate that dynamic trustworthiness significantly supports cooperation. Cooperators impede the incursion of defectors by progressively reducing their willingness to invest, thus fostering the formation of cooperative clusters. Our findings suggest that while sensitivity to higher payoffs bolsters cooperation, a tempered response to negative payoffs is advantageous. Additionally, the initial distribution of willingness is pivotal for the success of this dynamic. Our study expands the repertoire of strategy update techniques in investigating the evolution of cooperation and offers profound insights into the complexities of human cooperative behaviour.