Networks of Communities and Evolution of Cooperation

In this paper, we propose a new very simple mechanism supporting the emergence of cooperation in a population of memoryless agents playing a prisoner’s dilemma game. Each agent belongs to a community and interacts with the agents of its community and with the agents belonging to linked communities. A simple rule governs the dynamics of the system: a community grows (resp. decreases) if the average score of its members is superior (resp. inferior) to the average score calculated for the entire population. Starting from a random initialization, the system can evolve towards a majority of cooperators, towards the elimination of cooperators, or towards a situation with periodic evolutions of the populations of cooperators and defectors. The initial presence of clusters of C-strategies accounts for the convergence towards cooperative final states. We consider various topologies: Erdös and Rényi random graphs, square lattices and scale-free graphs. Clusters are not as likely to appear in all these topologies, so that there are significant differences between the average frequencies of cooperators associated with each topology. We show that random graphs favor cooperation whereas scale-free graphs tend to inhibit it. The relation between periodic evolutions and topological features is less clear. Nonetheless, we also state the importance of specific C-clusters for the survival of C-strategies in periodic oscillations. A major lesson of this paper is that the evolution of cooperation is very sensitive to initial conditions in models with global variables.