Dynamic analysis of weak prisoner's dilemma game considering conservative and aggressive cooperative strategy

The balancing of benefits is a critical pathway for maintaining cooperative relationships among selfish individuals within a group. Relevant research has confirmed that the ultimate outcomes of altruistic actions essentially revert to the level of self-interest. This study posits that individuals exhibit heterogeneous cooperative behaviors in social interactions due to differences in cognitive abilities and personality traits; accordingly, conservative cooperative strategy and aggressive cooperative strategy are introduced. Conservative cooperators are characterized by incurring additional identification costs when interacting strategically with other individuals, whereas aggressive cooperators demonstrate a higher level of resource investment to promote the emergence of cooperation. The results indicate that, in infinite well-mixed populations, reducing identification cost and increasing cooperative benefit can, to some extent, promote cooperation. In structured populations, especially under the random neighbor unconditional imitation rule, the relative advantages of the three strategies increase or decrease in a stage-dependent manner as the identification cost and aggressive cooperation cost vary. The research findings confirm that the presence of differentiated cooperative strategies effectively sustains group cooperation, providing new theoretical insights and model support for analyzing the mechanisms of cooperation evolution in real-world scenarios.