Spontaneous Symmetry Breaking in Interdependent Networked Game

TL;DR

This paper investigates how interdependence between two networks influences cooperation in spatial games, revealing a phase transition from homogeneous cooperation to symmetry breaking as interdependence increases.

Contribution

It introduces a model of interdependent networks for spatial games and analyzes the effects of interdependence on cooperation and symmetry breaking.

Findings

Homogeneous cooperation is guaranteed when interdependence is below a critical threshold.

Spontaneous symmetry breaking occurs when interdependence exceeds the threshold.

Results are accurately predicted by the strategy-couple pair approximation method.

Abstract

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.