Heterogeneous indirect reciprocity promotes the evolution of cooperation in structured populations

A fundamental aspect of all biological system is cooperation. Human society is based to a large extent on mechanisms that favor cooperation. Indirect reciprocity is a crucial factor for the emergence and maintenance of cooperation in evolutionary games. In this work, we introduce a mechanism of heterogeneous indirect reciprocity in the prisoner’s dilemma game, where an altruistic attribute is considered. The so-called altruistic attribute refers to the trait that when an altruistic individual cooperates, its neighbors, regardless of their strategies, can gain additional benefits. Intuitively, altruistic cooperative agents seem to do only what is beneficial for others, but in fact, their neighbors tend to cooperate in order to maintain the cooperative strategies of altruistic individuals. In this way, the neighbors of cooperative altruistic individuals not only guarantee their own additional benefits, but also indirectly protect the income of altruistic individuals, which strengthens the links between coop...