Growing Networks Driven by the Evolutionary Prisoner’s Dilemma Game

In this chapter, we present a model of growing networks in which the attachment of nodes is driven by the dynamical state of the evolving network. In particular, we study the interplay between form and function during network formation by considering that the capacity of a node to attract new links from newcomers depends on a dynamical variable: its evolutionary fitness. The fitness of nodes are governed in turn by the payoff obtained when playing a weak Prisoner’s Dilemma game with their nearest neighbors. Thus, we couple the structural evolution of the system with its evolutionary dynamics. On the one hand, we study both the levels of cooperation observed during network evolution and the structural outcome of the model. Our results point out that scale-free networks arise naturally in this setting and that they present non-trivial topological attributes such as degree-degree correlations and hierarchical clustering. On the other hand, we also look at the long-term survival of the cooperation on top of these networks, once the growth has finished. This mechanism points to an evolutionary origin of real complex networks and can be straightforwardly applied to other kinds of dynamical networks problems.