Cautious strategy update promotes cooperation in spatial prisoner’s dilemma game

In the realistic world, individual cautiousness can be often involved or observed when a rational individual makes a decision. However, it remains unclear how such individual cautiousness influences the evolution of cooperative behavior. To this end, we consider a Fermi strategy updating rule, where each individual is assigned a cautiousness index that controls its learning activity, and then study the evolution of cooperation in the spatial prisoner’s dilemma game. Interestingly, it is found that cooperation can be significantly promoted when individuals’ cautiousness is considered. In particular, there exists an optimal range of the degree of cautiousness resulting in the highest cooperation level. The remarkable promotion of cooperation, as well as the emerging phase transition is explained by configurational analysis. The sensitivity of cooperation to initial states with different fractions of cooperators is also discussed. The result illustrates that high densities of cooperators can be established at small initial fractions of cooperators. The detailed mechanism for such phenomenon is explained by analyzing the typical initial configurations.