Effects of Empty Sites on Cooperation in the Prisoner’s Dilemma Game Based on Social Diversity

Figure 5

Relative density of cooperators 𝜌_𝑐/𝜌 in dependence on the fraction of A players 𝜇 for different values of 𝜌 when 𝑏=1.15 and 𝛼=3.0 (see legend). Depending on the region of 𝜌, the optimum values 𝜇 that maximize the fraction of cooperators are different: for a larger occupation fraction, there are two maximum values. For example, two maximum values approximately occur at 𝜇=0.28 and 0.72 when 𝜌=0.9, respectively. However, for a smaller occupation fraction, for example, 𝜌=0.8 or 0.7, there is only one maximum value that approximately occurs at 𝜇=0.5.