Spatial structure favors cooperative behavior in the snowdrift game with multiple interactive dynamics

Spatial reciprocity is generally regarded as a positive rule facilitating the evolution of cooperation. However, a few recent studies show that, in the snowdrift game, spatial structure still could be detrimental to cooperation. Here we propose a model of multiple interactive dynamics, where each individual can cooperate and defect simultaneously against different neighbors. We realize individuals’ multiple interactions simply by endowing them with strategies relevant to probabilities, and every one decides to cooperate or defect with a probability. With multiple interactive dynamics, the cooperation level in square lattices is higher than that in the well-mixed case for a wide range of cost-to-benefit ratio r, implying that spatial structure favors cooperative behavior in the snowdrift game. Moreover, in square lattices, the most favorable strategy follows a simple relation of r, which confers theoretically the average evolutionary frequency of cooperative behavior. We further extend our study to various homogeneous and heterogeneous networks, which demonstrates the robustness of our results. Here multiple interactive dynamics stabilizes the positive role of spatial structure on the evolution of cooperation and individuals’ distinct reactions to different neighbors can be a new line in understanding the emergence of cooperation.