Adaptive multilayer networks resolve the cooperation dilemma induced by breaking the symmetry between interaction and learning

We study the coupled dynamics between strategy updating and partner switching on adaptive multilayer networks whose structure is split into an interaction layer for accumulating payoff and a learning layer for updating strategy. Two different types of adaptive multilayer network dynamics are modeled to study the evolution of cooperation. First, the selected individual either varies his strategy updating environment or switches his interaction partners during the partner switching process. It is proved that an increasing ratio of interaction network reconfiguration facilitates the coevolution of cooperation, indicating that interaction network acts a profound role in promoting the coevolution cooperation. Furthermore, we consider a type that the selected player simultaneously updates his strategy updating network and interaction network during the rewiring process. For a low frequent partner switching process, it is found that the evolution of cooperation is hindered whenever the two layers do not coincide. However, when the frequency of partner switching process increases, breaking the symmetry between interaction network and learning network resolves the social dilemma and enhances the evolution of cooperation. Moreover, a comparison between two adaptive multilayer network dynamics shows that the former type that only permits one layer to evolve every step on the adaptive multilayer networks suppresses the evolution of cooperation.