Heterogeneity of inferring reputation probability in cooperative behaviors for the spatial prisoners' dilemma game

As an important mechanism designed to counteract temptation and promote cooperation, reputation is widely investigated in the spatial Prisoners' dilemma game. Existing research assumes that each agent imitates the neighbor that has the highest reputation with an inferring reputation probability pi, which is heterogeneous and enhances cooperation to some extent. So far the effect of heterogeneity has not been adequately revealed. Therefore, we will inspect the heterogeneity effect on a square lattice where agents play the prisoners' dilemma game. It is assumed that the inferring reputation probability is normally distributed, and its mean p and standard deviation sd represent its mean effect and heterogeneity effect on cooperation. Simulation results demonstrate that the mean or overall effect on cooperation fits a nonlinear relationship. It promotes cooperation substantially as the mean is smaller (p<0.5), it stabilizes cooperation at a stable state as the mean is in the middle range, and it undermines cooperation while p is larger (p>0.8). The heterogeneity effect varies with p as well: In the whole range of p, sd neither promotes nor reduces cooperation. However, heterogeneity reduces cooperation when p is smaller (p<0.5), but turns to increasing cooperation when it grows larger (p⩾0.5).