Evolution Of Cooperation In Prisoner’s Dilemma Game Under The Coupling Of Aspiration And Imitation Rules

Nowadays,evolutionary game theory is a powerful method to study cooperative behavior.Based on the above background,this paper studies the effect of the updating mechanism coupling aspiration and imitation rules on cooperation.Considering the important roles played by aspiration and imitation rules,we explore how cooperation evolves in the spatial prisoner’s dilemma game.In detail,the strategy updating rule couples the inner aspiration payoff and the external neighbors payoff through the parameter α.Intriguingly,we find that there exists an optimal value of a leading to the highest density of cooperators for each aspiration level A.By analyzing the dynamical strategy changes of system,we find that an optimal a helps individuals form cooperator clusters and curbs the further spread of high-payoff defectors,and thus improves the density of cooperators.Moreover,when 0.1≤A≤0.5,the optimal value of α,which leads to the highest density of cooperators,decreases with A,the optimal range of a gradually expands and the highest cooperation level is on the rise.At the optimal value of α,the individual strategy change frequency Nr=0 is an innovative point of this paper,when the cooperaton level is stabilized at the highest level and all individuals do not change their strategies,which is a special kind of static stability.Based on the updating mechanism for coupling aspiration and imitation rules,this paper further explores the evolution of cooperation on the WS small-world network.Simulation results show that there is also an optimal value of a to improve the cooperation level and achieve full cooperation state on the WS small-world network.In detail,when 0.2≤α≤0.8 and 0.1≤A≤0.4,the density of cooperators reaches the highest level,and the group is in full cooperation state.In addition,we explore the influence of the rewiring probability p on evolution dynamics on the WS small-world networks.The results show that the higher the rewiring probability p,the higher the cooperation level on the WS small-world networks.