Towards a model of the human society: A theoretical solution of the cooperation problem

In this paper we address the cooperation problem in structured populations by considering the prisoner's dilemma game as metaphor of the social interactions between individuals with imitation capacity. We present a new strategy update rule called democratic weighted update where the individuals 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 wisdom which is defined by its successful in the game. 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 total wisdom 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 shown that the social influence allows to overcome the emergence of mutants into highly cooperative systems. In this way, we are able to conclude that considering the growing process of the system, individuals with imitation capacity and the social influence the cooperation evolves. Therefore, here we present a theoretical solution of the cooperation problem among unrelated individuals with imitiation capacity.