The effect of memory in prisoner's dilemma game under multi-strategy update mechanism

Due to the heterogeneity of strategy updating rules progressively destroying the cluster of cooperators, cooperation would be heavily suppressed when players adopt mixed strategy updating rules. Thus, how to improve the emergence of cooperation with the scenario of heterogeneous strategy updating rules becomes an important open issue. In this paper, we introduce the memory factor into the game model, and then study the joint effect of memory and heterogeneous strategy updating rules on the emergence of cooperation. Detailly, in our game model, memory-based imitation and innovation are chosen as two different strategy updating rules. Afterwards, the annealing and quenching rules are specifically used as the methods to mix the proposed two memory-based strategy updating rules. At last, Monte Carlo simulations are conducted to demonstrate the significance of our model. The simulation results show that for memory-based imitators, memory is not always effective in promoting cooperation. It's more like a catalyst. When the proportion of the memory-based imitation is large, it promotes the emergence of cooperation. When the proportion of innovation is large, it accelerates the extinction of cooperation; for overall proportion of cooperation, memory effectively promotes the emergence of cooperation and improves the ability of cooperators to resist high temptation, but memory is a partial optimization, it cannot offset the deterioration of cooperation caused by heterogeneous strategies updating rules, memory only reduces the degree of deterioration. Finally, compared with the annealing rule, the change of quenching rule is more smooth, because it is easier for cooperators to form clusters under the quenching rule. Our investigation sheds some light to the role of memory in prisoner's dilemma game under heterogeneous strategies updating rules.