Identifying influential agents is an important issue in controlling the dynamical processes in complex networks, while centrality measurements are good ways to rank node’s influence. In this paper, we combine agents’ influence with their strategy-updating timescales to explore the effect of diverse influences on the emergence of cooperation in the evolutionary prisoner’s dilemma game. Through Monte Carlo simulation in five real-world social networks, we find that collective influence outperforms the basic centrality measurements such as degree and coreness in ranking agent’s influence, identifying the influential spreaders and promoting the evolution of cooperation. Moreover, collective influence with depth length plays an nontrivial role on the evolution of cooperation in networked systems.

Based on the Prisoner's Dilemma game, we study the effect of the diverse strategy-updating time scale on the evolution of cooperation under the normalized payoff framework. Agents can adjust their strategy-updating speed according to their fitness and collective influence, and this mechanism promotes the emergence of cooperation on Barabási-Albert scale- free networks. Moreover, agents with higher values of collective influence may have longer persistence-cooperation duration and diffuse their cooperative behaviors among neighbors efficiently. Through investigating the game-learning skeleton, we find that the heavy-tailed in-degree distribution emerges and influencers with proper depth length play an important role in maintaining cooperation.

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.

Based on the celebrated Prisoner's Dilemma game, we study the roles of mutation mechanism for the evolution of cooperation with extortion strategies on clustered scale-free networks. It is shown that cooperation can be promoted under the influence of extortion strategies with small mutation rate. This is because that mutation helps the formation of alliance between extortion and cooperation strategies, and extortioners tend to locate on hubs and induce more small-degree neighbors becoming cooperators on high clustered scale-free networks. However, too smaller or too larger mutation rates will inhibit the emergence of cooperation, and the positive influence of mutation on the cooperation disappears on low clustered scale-free networks. This work may provide some clues to explore efficient methods to optimize performance on networked systems.

Based on the celebrated public goods game with group interaction, we study the evolution of cooperation on two kinds of scale-free networks with similar degree distribution and clustering coefficient. It is showed that there are different evolution routes in the structured population. The metric clusters existing on the popularity-similarity network let cooperation diffuse in local regions. Whereas, cooperators on the clustered scale-free network tend to invade hubs firstly, and then spread from hubs to leaves with a top-down pattern, which leads to the higher cooperation level on the clustered scale-free network than that on the popularity-similarity network.

Extortion strategies, which can let an individual's surplus exceed her opponent's by a fixed percentage, have played an important role in the understanding of the evolution of cooperation in the Prisoner's Dilemma game. In this paper, we combine individuals' extortion ability with their degrees, and study the influence of extortion diversity in the heterogeneous scale-free network. Our investigation shows that, when individuals' extortion factors are negative correlation with their degrees, these extortionate hubs play as catalysts to enhance the emergence of cooperative behavior. However, when the extortion factors are positively correlated with degrees, the effect of hub's catalyst is weaken.