The effects of heterogeneity of updating rules on cooperation in spatial network

The emergence and maintenance of cooperation remains to be one of the overreaching problems and a number of scholars have devoted endless efforts to resolve such problems. To further explore this issue, we focus on the impact of heterogeneity of updating rules on cooperative behavior in voluntary prisoner's dilemma; here, two types of strategy updating rules are considered to mimic social facts which are listed as strategy learning mechanism and strategy teaching mechanism. The stability of different mechanisms on promoting cooperation is thoroughly investigated in this manuscript. Numerical simulations are conducted while corresponding results are presented with sufficient clarifications. We find that the strategy learning mechanism can promote cooperation steadily. However, with the variance in the proportion of the two update rules in the investigated community, the strategy teaching mechanism seems to be more sensitive. Moreover, compared with strategy learning mechanism, strategy teaching mechanism plays a more important and apparent role in promoting cooperation. We also find that personal strategy is sensitive to the varying of Loner's payoff σ, especially when σ is close to 1. We hope our findings will shed some lights on resolving the social dilemmas.