The Evolution of Submissive Strategies on the Clustered Scale-Free Networks

Network reciprocity is an important mechanism to explore the ubiquitous cooperative behaviors in the natural and social systems, and the scale-free and clustered properties play important roles on the evolution of cooperative behaviors. Sub-missive strategies are a kind of zero-determinant strategies, which can unilaterally guarantee the submissive agent's payoff not more than its opponent. Besides they can reach mutual cooperation with cooperative strategies, thus they attract much attention. In this work, we study the evolution of submissive strategies in competition with defection on the clustered scale-free networks. Our investigation shows that part of the submissive strategies can dominate defection on the clustered scale-free network under both accumulated and normalized payoff frameworks. Particularly, under the accumulated payoff framework, clustered scale-free networks with high values of the clustering coefficient promote the emergence of submissive strategies, but under the normalized payoff framework, submissive agents eliminate defection in the clustered scale-free networks with low values of clustering coefficient.