The Prisoner’s Dilemma Game on Random Scale-Free Networks

Abstract

As it has been well established in previous chapters, when implementing the Prisoner’s Dilemma (PD) game on top of complex networks, the scale-free (SF) topologies greatly enhance cooperation [1–12], compared to other topologies as ER networks. It is also well known that the heterogeneity on the degree distribution of these structures is a crucial factor in order to achieve such high levels of cooperation in the system. More specifically, the hubs, or nodes with the highest connectivity, act always as cooperators, surrounding themselves with middle-class cooperators, and creating a unique cluster (or ‘Eden’) of cooperation that is able to resist the attack of defectors, even when cooperation gets really expensive. Nonetheless, up to now we have only focused on the BA model [13], among other SF network models available in literature (for a quick review of some of them, see [14, 15]). BA SF networks have some correlations by construction, the so-called age-correlations [16, 17, 18]. That means that older nodes, the ones that arrived earlier to the system when it was being built are interconnected, since they formed the original core of nodes, and besides, these older nodes usually become hubs as the network grows. The existence of age-correlations can be found in some real systems also, such as the collaboration or citation networks, or the ’old boy’ network, made up of former students of the Ivy League that now work at the top investment banks [19].