Cooperation and its evolution in growing systems with cultural reproduction

We explore the evolution of cooperation in the framework of the evolutionary game theory using the prisoner's dilemma as metaphor of the problem. We present a minimal model taking into account the growing process of the systems and individuals with imitation capacity. We consider the topological structure and the evolution of strategies decoupled instead of a coevolutionary dynamic. We show conditions to build up a cooperative system with real topological structures for any natural selection intensity. When the system starts to grow, cooperation is unstable but becomes stable as soon as the system reaches a small core of cooperators whose size increase when the intensity of natural selection decreases. Thus, we reduce the emergence of cooperative systems with cultural reproduction to justify a small initial cooperative structure that we call cooperative seed. Otherwise, given that the system grows principally as cooperator whose cooperators inhabit the most linked parts of the system, the benefit-cost ratio required for cooperation evolve is drastically reduced compared to the found in static networks. In this way, we show that in systems whose individuals have imitation capacity the growing process is essential for the evolution of cooperation.