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

Figure 6

Relative density of cooperators 𝜌_𝑐/𝜌 against 𝛼 for different values of 𝜌 when 𝑏=1.15 and 𝜇=0.5 (see legend). For the lower occupation densities, for example, 𝜌=0.4, all isolated cooperator clusters are able to survive for all the values of 𝛼. But it is worth noting that the relative density of cooperators varies nonmonotonically with the increase of 𝛼 when 𝜌>0.4, which indicates that moderately enlarging the gaps among the social ranks can facilitate cooperation, while exceedingly large or small gaps inhibit cooperation. Moreover, although cooperation is possible in a wide range of 𝛼 for 0.6≤𝜌<1, cooperation performs best when 𝜌=0.8.