Evolutionary game on a growing multilayer network

Abstract Numerous complex systems display the multilayer feature rather than the single or isolated one. It is thus significant to study how these structures emerge and the mechanisms behind them. In this paper we propose a novel growing model to explain the formation of multilayer networks, where the network growth and strategy evolution in prisoner’s dilemma game interact and coevolve. We introduce the growing rate to control the ratio of strategy evolution to network growth, and the coupling strength to adjust the connecting density between layers. The simulation results show that besides the scale-free property observed in the resulting networks, the coupling strength is significant to cooperative behaviors. Under the weak coupling strength, the role of network reciprocity works and the resulting networks can preserve a relatively high cooperation level; however, with the increase of coupling strength, the role of network reciprocity fades away or disappears. The strong coupling strength, denoting individuals can obtain more extra payoff from their external circumstance, induces a low cooperation level. In addition, the growing rate also influences cooperative behaviors and a fast growing rate is beneficial to cooperation.