We study the evolution of cooperation in public goods games on the square lattice, focusing on the co-player learning mechanism based on the preferential selection that are brought about by wealthy information of groups where participants collect and search for potential imitators from those groups. We find that co-player learning mechanism based on the choice of weighted group can lead to the promotion of public cooperation by means of the information of wealthy groups that is obtained by participants, and after that the partial choice of public goods groups is enhanced with the tunable preferential parameter. Our results highlight that the learning interactions is not solely confined to the restricted connection among players, but co-players of wealthy groups have the opportunity to be as a role model in the promotion of cooperative evolution. Moreover, we also find the size of learning affects the choice of distant players, cooperators (defectors) having more paths to exploit the phalanx of opponents to survive when the value of preferential parameter is small. Besides, the extinction thresholds of cooperators and defectors for different values of noise are also investigated.
Particle swarm intelligence and the evolution of cooperation in the spatial public goods game with punishment
