Evolution of Cooperation in the Memory-based Multigame on Complex Networks

Understanding the emergence of cooperation in society is an open problem. In response to this problem, the network evolutionary game and its derivatives, such as multigame, have been shown to be an effective method to address social dilemmas. In this paper, we investigate the memory-based multigame consisting of the prisoner's dilemma game and the snowdrift game on the square lattice with periodic boundary and small-world networks. Plus, we also propose a novel strategy-updating rule by combining the player's memory mechanism and replicator dynamics. Subsequently, we conduct simulations to demonstrate the effects of the payoff parameters and players' memories on network cooperation behavior. Our results show that by introducing the memory mechanisms and multigame, cooperation can occur widely on complex networks.