Cooperation and its emergence in growing systems with cultural reproduction

We explore the emergence of cooperation in the framework of evolutionary game theory. First we introduce the cooperation problem in a novel way that we believe it have important consequences in how problem is addressed. Then we present a minimal model for the emergence of cooperation in growing systems with cultural reproduction where topological structure and the evolution of strategies are decoupled instead a coevolution dynamic. We show that when system grows, there exists cultural reproduction and a nonzero probability that individuals take cooperation as first strategy; there are conditions to build up a cooperative system with real topological structures for any natural selection intensity. When the system is small cooperation is unstable but become stable as soon as the system reaches an enough well defined topological structure which size mainly depends on the intensity of natural selection. In this way, we reduce the emergence of cooperation problem for systems with cultural reproduction to justify a small initial cooperative structure, what we call cooperative seed. Otherwise, given that the system grows principally as cooperator whose cooperators inhabit the most linked parts of the system, the condition required to cooperation prevails into the systems are drastically reduced compared to those found in statics networks.