Spontaneous Symmetry Breaking in Interdependent Networked Game

Spatial evolution game has traditionally assumed that players interact with neighbors on a single network, which is isolated and not influenced by other systems. We introduce the simple game model into the interdependent networks composed of two networks, and show that when the interdependent factor $\alpha$ is smaller than a particular value ${\alpha }_C$, homogeneous cooperation can be guaranteed. However, as interdependent factor exceeds ${\alpha }_C$, spontaneous symmetry breaking of fraction of cooperators presents itself between different networks. In addition, our results can be well predicted by the strategy-couple pair approximation method.