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

Figure 3

Relative density of cooperators 𝜌_𝑐/𝜌 in dependence on the occupation fraction 𝜌 for the different fractions of A players 𝜇 when 𝛼=3.0 and 𝑏=1.15 (see legend). Irrespective of the values of 𝜇, the relative fraction of cooperators decreases from around 0.47 with the increase of 𝜌, and then the curves for different values of 𝜇 depart around 𝜌=0.1. For 𝜇=0, the relative density of cooperators decreases monotonically with the increase of 𝜌 until approaching zero. When 𝜇 is equal to 0.1 or 0.2, the relative density of cooperators decreases monotonically with the increase of 𝜌 until approaching its minimum value and then increases monotonically with the increase of 𝜌 until approaching its maximum value at 𝜌=1.0. In contrast, when 𝜇 is equal to 0.5, the relative density of cooperators decreases monotonically with the increase of 𝜌 until approaching its minimum value, then increases monotonically with the increase of 𝜌 until approaching its maximum value at around 𝜌=0.8, and finally sharp decreases with the increase of 𝜌 until approaching its minimum value at 𝜌=1.0.