Co-evolution mechanism in networked snowdrift game with large connection range

Interactive networks play an important role in evolution of cooperation. Compared to traditional game performed on static network, co-evolutionary game models can capture the dynamic interactive connection between players. Aiming to depict more realistic network dynamics, we propose a co-evolutionary game model that incorporates three features describing the entire connection updating process: (1) Selection range adjustment, expanding or reducing players’ neighbor selection ranges based on their payoffs; (2) Preferential selection, favoring connection with the most successful players while severing connection with low-payoff player with a certain probabilities; (3) Mutual connection willingness, requiring the consent of both players for new connections. Note that these features jointly facilitate the appearance of large connection range, which frequently emerges in real-world systems. Experimental results show that the proposed mechanism can drastically enhance cooperation level of snowdrift game with wide ranges of all parameters. More interestingly, the co-evolution process reveals how a scale-free network evolves from the initial lattice structure, providing new insights into realistic co-evolution dynamics. It is also shown that large connection ranges are essential for both high-level cooperation and scale-free network emergence.