Cooperation Dynamics Research On Interdependent Networks Based On The Prisoner's Dilemmaand Snowdrift Game

In recent years, complex network has been studied more and more, in real life, many complex systems can be abstracted as complex networks. In order to have a deep understanding on various dynamics process in complex systems in real life, we introduce the evolutionary game theory into complex network.Evolutionary games is always studied on single-layer networks before. However in real life, the individual may participate in the different social network, so the research of cooperation evolution in multilayer network has important practical significance.In this work, we study evolutionary games in two-layer networks by introducing the correlation between two layers through the C-dominance or the D-dominance. We assume that individuals play the Prisoner's Dilemma game (PDG) in one layer and the Snowdrift game(SDG) in the other. We explore the dependence of the fraction of the strategy cooperation in different layers on the game parameter and initial conditions. The results on two-layer square lattices show that, when cooperation is the dominant strategy, initial conditions strongly influence cooperation in the PDG layer while have no impact in the SDG layer.Moreover, in contrast to the result for PDG in single-layer square lattices,the parameter regime where cooperation could be maintained expands significantly in the PDG layer. When defection is the dominant strategy,initial conditions strongly influence cooperation in the PDG layer and the SDG layer. And as the growth of the variation parameter, cooperation in the PDG layer and the SDG layer shows negative correlation. We also investigate the effects of mutation and network topology. We find that different mutation rates do not change the cooperation behaviors.Moreover, similar behaviors on cooperation could be found in two-layer random networks. Finally, we introduce mixing dominant strategy in our model, and find that mixing dominant strategy is bad for the evolution of cooperation in the PDG layer. Interestingly, in the SDG layer, there may exist an optimal mixing dominant strategy maximizing the proportion of cooperators.