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

Figure 2

Relative density of cooperators 𝜌_𝑐/𝜌 in dependence on the occupation fraction 𝜌 for different values of 𝑏 when 𝜇=0.5 and 𝛼=3 (see legend). Irrespective of the value of 𝑏, the relative density of cooperators 𝜌_𝑐/𝜌 decreases from around 0.485 with the increase of 𝜌, and then the curves for different values of 𝑏 depart around 𝜌=0.1. Still further, there are three interesting cases: the first interesting case occurs if 𝑏 = 1.0, where the relative density of cooperators 𝜌_𝑐/𝜌 increases monotonically with the increase of 𝜌 until approaching a unity; the second interesting case occurs if 𝑏 is in the region, 1.05<𝑏≤1.175, where the relative density of cooperators increases monotonically with the increase of 𝜌 until reaching its maximum value and then sharp decreases; the third interesting case appears if 𝑏 is in the region 𝑏>1.175, for example, 𝑏=1.2, where the relative density of cooperators decreases monotonically with the increase of 𝜌 until approaching zero.