Interplay between Network Growing and Benefit Competition

In a competitive environment, the formation of network structures is not only related to the preferential linking but also the multiple state of interacting agents. With an adjustable parameter controlling the growth of networks, we study the correlations between the commonly observed topological properties of networks and the configuration of individual states. Numerical simulations show that a cooperative environment promotes the formation of scalefree networks. In an uncooperative environment, a large number of benefit-pursuing agents make equally distributed connections and the topological property of the network exhibits exponential node degree sequences. The mean field theory is applied to predict the growth of networks and analytical calculations are in accordance with simulation results.