Promotion of cooperation in the form C₀C₁D classified by 'degree grads' in a scale-free network

In this paper, we revisit the issue of the public goods game (PGG) on a heterogeneous graph. By introducing a new effective topology parameter, 'degree grads' φ, we clearly classify the agents into three kinds, namely, C ₀, C₁, and D. The mechanism for the heterogeneous topology promoting cooperation is discussed in detail from the perspective of C ₀C₁D, which reflects the fact that the unreasoning imitation behaviour of C₁ agents, who are 'cheated' by the well-paid C₀ agents inhabiting special positions, stabilizes the formation of the cooperation community. The analytical and simulation results for certain parameters are found to coincide well with each other. The C₀C ₁D case provides a picture of the actual behaviours in real society and thus is potentially of interest.