Effect of expanding learning scope on the evolution of cooperation in scale-free networks

We study how expanding the scope for selecting game and learning (adaptation) partners affects the evolution of cooperation in public goods games on scale-free networks. We show the following three results. (i) Expanding the scope for selecting game partners suppresses cooperation. (ii) Expanding the scope for selecting learning partners promotes cooperation when cooperation evolution is difficult. (iii) When cooperation is more likely to evolve, slightly expanding the scope for selecting learning partners causes a significant drop in the cooperation rate, but expanding the scope further causes the cooperation rate to recover. Although (i) is explained by the hub-centered mechanism, the well-known dynamic that promotes cooperation on scale-free networks, (ii) and (iii) are caused by a completely different mechanism that has heretofore been rarely mentioned.