While many people believe in egoism and protectionism, the concept of "win-win cooperation" is widely accepted worldwide. Investigating how cooperation behavior emerges and evolves can help us understand the interaction mechanism in human society.

In evolutionary game theory (EGT), the traditional methods are the Replicator equation and the Moran Model. However, these methods have limitations as they do not adequately consider the impact of network topology.

This thesis aims to investigate the cooperation behavior in different network topologies using analysis and modelling methods.

Networks in EGT are high-level representations of intricate systems, capturing the individuals in a real complex system and the relationships between them as nodes and connected edges. Each node can adopt one of two strategies: Cooperation or Defection. Nodes can also alter their strategies based on max-payoff strategy updating rule. Cooperation behavior is analyzed through the cooperation percentage during the generation.

We began by examining well-mixed populations. We then explored homogeneous network games. The results show that in well-mixed and circle networks, defection is the only stable state. However, in grid networks, there exists an infinite coexistence of cooperation and defection, which has a threshold on the size of the grid networks.

Lastly, we expanded our investigation to heterogeneous network games. Through numerical simulations, we demonstrated that both cooperation and defection can be stable states. We also discovered that heterogeneity does not directly promote cooperation, but rather indirectly influences it through the "celebrity effect".