Co-evolution of strategies and update rules in the prisoner's dilemma game on complex networks

In this paper, we study a weak prisoner's dilemma (PD) game in which both strategies and update rules are subjected to evolutionary pressure. Interactions among agents are specified by complex topologies, and we consider both homogeneous and heterogeneous situations. We consider deterministic and stochastic update rules for the strategies, which in turn may consider single links or the full context when selecting agents to copy from. Our results indicate that the co-evolutionary process preserves heterogeneous networks as a suitable framework for the emergence of cooperation. Furthermore, on those networks the update rule leading to a larger fraction, which we call replicator dynamics, is selected during co-evolution. On homogeneous networks, we observe that even if the replicator dynamics again turns out to be the selected update rule, the cooperation level is greater than on a fixed update rule framework. We conclude that for a variety of topologies, the fact that the dynamics co-evolves with the strategies leads, in general, to more cooperation in the weak PD game.