The roles of particle swarm intelligence in the prisoner’s dilemma based on continuous and mixed strategy systems on scale-free networks

摘要

Understanding and explaining the widespread emergence of cooperation in social dilemmas remains a great challenge. Previous researches have shown that complex networks with high heterogeneity especially scale-free networks can remarkably facilitate cooperation in the case of accumulated payoff, but fail in the case of average payoff. In this paper, we investigate the role of particle swarm optimization (PSO) strategy update rules in the evolution of cooperation in the prisoner’s dilemma (PD) on scale-free networks, when each player obtains the average payoff normalized with its degree. In the meantime, considering whether goods and resources are divisible, PSO strategy update rules based on continuous and mixed strategy systems are proposed respectively. The simulation results show that the PSO strategy update rules can promote cooperation in the continuous strategy system, but lead to the severe collapse of cooperation in the mixed strategy system. The nodes with low or medium degree play an important role to facilitate cooperative behaviors.