The cooperation evolution in a three-strategy model including enforcers with the ability to reward, punish and assess

Social governance plays a pivotal role in maintaining social stability and harmony, with law enforcers serving as crucial actors in this process. This study introduces a novel three-strategy evolutionary game model incorporating an enforcement strategy, where enforcers adopting the enforcement strategy obtain mutually beneficial payoffs when interacting with cooperators, but incur mutual losses when engaging with defectors. And enforcers can make behavioral evaluations of individuals based on their historical performance. Numerical experiments show that the presence of enforcers can suppress defection and promote cooperation. Interestingly, it is also found that increasing the reward and intensifying the punishment are not always beneficial for cooperation. Moreover, under a certain reward and punishment environment, interesting cooperative emergence phenomenon also occurs in the system in the process of increasing the social dilemma. This study is helpful for understanding the role of enforcers in the evolution of three-strategy dilemma games and the mechanism of cooperation emergence.