Evolution of cooperation in a heterogeneous population with influential individuals

Influential individuals are introduced and integrated with the public goods game (PGG) to investigate their influence on the emergence and evolution of cooperation. In the model, some influential individuals whose behaviors can be controlled by us are introduced into a homogeneous population on a square lattice. The influential individuals can play three kinds of roles: I. exemplar, II. supervisor with the power to punish defectors, and III. supervisor with the power to reward cooperative co-players. It is found that the existence of influential individuals who play Role I turns out to be detrimental to cooperation and that the larger the number of influential individuals is, the more difficult it is for cooperation to be maintained. For those playing supervisory roles, both punishment and reward are found to be effective ways for the influential individuals to promote and stabilize cooperative behavior. By comparing the critical costs and the mean payoffs for a low multiplication factor under the role of punishment and the role of reward, it is found that reward is a more effective intervention measure than punishment for influential individuals seeking to improve cooperation and that reward leads to a higher mean payoff.