Effect of the degree correlation in public goods game on scale-free networks

We study the influence of degree correlation on the evolution of cooperation in the networked public goods game (PGG). With the aid of the analysis of the PGG on a double-star graph, we are able to investigate intuitively how the degree mixing patterns affect the transformation of individuals' strategies. We find that the assortative mixing among the individuals inhibits the emergence and sustainment of the cooperation, due to fact that the distinct core-periphery structure present in the assortative networks disable the hubs's ability to impact those remote leaf-vertices, and as a result the defection is easy to diffuse among them. In the disassortative networks, however, we observe that the absence of communication among the hubs cause them to almost keep their initial strategies, which is helpful for cooperators to persist in the case of very low multiplication factor of the PGG.