Cooperative networks overcoming defectors by social influence

We address the cooperation problem in structured populations by considering the prisoner's dilemma game as a metaphor of the social interactions between individuals with imitation capacity. We present a new strategy update rule called democratic weighted update where the individual's behavior is socially influenced by each one of their neighbors. In particular, the capacity of an individual to socially influence other ones is proportional to its accumulated payoff. When in a neighborhood there are cooperators and defectors, the focal player is contradictorily influenced by them and, therefore, the effective social influence is given by the difference of the accumulated payoff of each strategy in its neighborhood. First, by considering the growing process of the network and neglecting mutations, we show the evolution of highly cooperative systems. Then, we broadly show that the social influence allows to overcome the emergence of defectors into highly cooperative systems. In this way, we conclude that in a structured system formed by a growing process, the cooperation evolves if the individuals have an imitation capacity socially influenced by each one of their neighbors. Therefore, here we present a theoretical solution of the cooperation problem among genetically unrelated individuals.