Popularity enhances the interdependent network reciprocity

Interdependent networks (IN) are collections of non-trivially interrelated graphs that are not physically connected, and provide a more realistic representation of real-world networked systems as compared to traditional isolated networks. In particular, they are an efficient tool to study the evolution of cooperative behavior from the viewpoint of statistical physics. Here, we consider a prisoner dilemma game taking place in IN, and introduce a simple rule for the calculation of fitness that incorporates individual popularity, which in its turn is represented by one parameter α. We show that interdependence between agents in different networks influences the cooperative behavior trait. Namely, intermediate α values guarantee an optimal environment for the evolution of cooperation, while too high or excessively low α values impede cooperation. These results originate from an enhanced synchronization of strategies in different networks, which is beneficial for the formation of giant cooperative clusters wherein cooperators are protected from exploitation by defectors.