Justice strategy can promote cooperation with the joint of dynamic aspiration in social dilemma

Abstract We investigate the concurrent effect of the justice strategy and dynamic aspirations on cooperation in evolutionary game theory. The justice strategy refers to a game in which players play the role of cooperators in the case of cooperation, the role of punishers in the face of defection, and receive the same payoff as their opponents. Players compare the payoffs with their own dynamic aspirations to decide whether to change their strategy. Through simulations, we demonstrate the effectiveness of our model in promoting cooperation and reducing or completely eliminating defections. A higher initial aspiration has a significant impact on reducing defection. Additionally, we find that diverse evolutionary dynamics arise from various initial settings. Remarkably, in specific situations, even a tiny initial fraction of justicers can rapidly retaliate and eventually dominate the entire system. Reflecting real-life scenarios, the influence of punishment typically lags behind the occurrence of defection, allowing justicers to gradually counteract defection upon its cluster emergence.