  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.
