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

Strategy update may involve costs or risks in evolutionary games since the new strategy may lead to a lower payoff and even a cascading failure in the future. Therefore, individuals may be cautious in the strategy updating process. Here we study the evolutionary prisoner’s dilemma game on a square lattice by the Fermi updating rule, where each individual is assigned a cautiousness index that controls its learning activity. Interestingly, it is found that cooperation can be significantly promoted when individuals are cautious to update strategy. 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 the configuration analysis. We also demonstrate the robustness of the promotion of cooperation with respect to the initial conditions consisting of different fractions of cooperators. Our study uncovers the nontrivial effect of individual cautiousness on cooperation, and thus provides an explanation of the ubiquitous cooperation from the perspective of individual characteristics.