The influence of individuals' movement and memory on the evolutionary cooperative behavior

Considering the influences of individuals' movement and memory, a modified prisoner's dilemma (PD) game model is proposed in this letter. The evolutionary equation of cooperator density is provided in terms of the mean-field theory firstly, and then the proposed model is performed on the lattice network. The numerical results show that if the individual's memory decay factor or memory length is large enough, it is beneficial to promote the cooperation between individuals. Meanwhile, when the population density is neither too dense nor too sparse, cooperative behavior can be effectively promoted. Finally, we show that the emergence of cooperation could be formed due to the movement of individuals. However, when the temptation gain T is extremely large, it is vulnerable to the invasion of cooperators. Our research could have certain enlightenment and reference value on the evolutionary game