Protection and improvement of indirect identity cognition on the spatial evolution of cooperation

In the public goods game on the network, individuals might believe that their neighbors’ neighbors have more similar situations to their own than their direct neighbors since they play games with the same individuals. Based on this assumption, we make individuals learn strategies from second-order neighbors and consider the neighborhood profits of other individuals with a certain probability as the basis for selecting their own neighbors, to propagate strategies and adapt the network structure while considering the self-identification of individuals. To study the effects of examining neighborhood profits on cooperation and network topology, we conduct simulations using different levels of examination intensity. A rich evolutionary landscape is observed led by different parameter combinations. When the individual’s consideration intensity of neighborhood profit is low, cooperation will increase with higher intensity. However, cooperation will be inhibited if an individual considers neighborhood profit moderately. Furthermore, if the individual’s consideration of neighborhood profit is strong, the complexity of the network structure will emerge spontaneously, and the protection of cooperation will occur. In addition, we have observed the separation of degree distribution among individuals in different strategies in the evolution. The results imply the inner principle of the protection mechanism for cooperation existing in reality, and the coupling between the formation of network complexity and the promotion of cooperation.