Preferential selection to promote cooperation on degree–degree correlation networks in spatial snowdrift games

Degree–degree correlation is an important topological characteristic of real-world networks and has been shown to have a significant effect on cooperation in a population. Meanwhile, the preferential selection of individuals could be exploited as an effective mechanism to improve cooperation in evolutionary games. Network structure and strategy evolution are two essential factors affecting the level of cooperation in spatial evolutionary games, and by considering both of them, proposed here is a spatial snowdrift game with preferential selection on scale-free networks with degree–degree correlation. How two main parameters—the Pearson correlation coefficient r and the intensity of preferential selection δ—affect the cooperation is investigated, and simulation results show that when preferential selection is involved in evolutionary games, then larger δ can give a higher level of cooperation. Importantly, an optimal value of r is found that gives maximum cooperation in the population, and how r and δ affect the cooperation is found to depend on the cost parameter of the game. Furthermore, corresponding microcosmic explanations are provided based on the quantity χ, the time series of links, and the strategy distribution.