Evolutionary gambling dynamics for two growing complex networks

Abstract

The dynamic complex network is an important model of social structure and stability. Based on the single dynamic complex network, we propose a growing double-network evolutionary gambling model. When the two networks are separated, we find that the average of cooperation strategy has a jump as the payoff increases, which can be regarded as a phase transition. This result is a generalized result of static gambling network. When the two networks are connected, their averages of cooperation strategy are synchronized. When the intra-linkages are increased, the natural selection does not favor cooperation, while the fair selection does. When the inter-linkages are increased, the average of cooperation strategy decreases for both networks. As the ratio of inter- and intra- linkage is constant, the more the average degree, the less the cooperation. We find the existence of defection leader, and uncover its influence on the average of cooperation strategy and how it interacts with cooperation leader. These results provide some hints to understand the social structure, stability and evolution.