No Scale Evolutionary Game On The Network Study

Cooperation universally exists in the natural and social communities. According to Darwin's theory, the altruistic individuals should be eliminated due to altruistic actions with the cost of lowing down their own fitness. So how to understand the rise of cooperation in the context of Darwin's theory? This is a basic problem of evolutionary games in complex networks.In the paper,we firstly investigate the cooperative behaviors on the structured scale-free network. On the contrary of the conventional wisdom that scale-free networks are prone to cooperation spreading, the evolution of cooperation is inhibited on the structured scale-free network while performing the prisoner's dilemma (PD) game. We demonstrate that neither the scale-free property nor the high clustering coefficient is responsible for the inhibition of cooperation spreading on the structured scale-free network. Then we provide one heuristic method to argue that the lack of age correlations and its associated'large-world'behavior in the structured scale-free network inhibit the spread of cooperation.Due to the difference of cooperative behaviors in the various scale-free networks, we further investigate what role the scale-free property itself plays in the evolutionary games.Then we apply PD and public goods game (PGG) on a family of scale-free networks with exactly the same degree sequence. Experiment results present various demonstrations of cooperative frequency for different members in the above scale-free network family although they share the identical degree sequence.After careful analysis,we find out it is the difference in the number of direct connections among large degree nodes that causes the numerical results vary so much. So we argue that the scale-free degree distribution property alone could not be the decisive factor responsible for the prevailing cooperative behaviors on social networks.