  It is well known that cooperation cannot be an evolutionary stable strategy
for a non-iterative game in a well-mixed population. In contrast, structured
populations favor cooperation since cooperators can benefit each other by
forming local clusters. Previous studies have shown that scale-free networks
strongly promote cooperation. However, little is known about the invasion
mechanism of cooperation in scale-free networks. To study microscopic and
macroscopic behaviors of cooperators' invasion, we conducted computational
experiments of the evolution of cooperation in scale-free networks where,
starting from all defectors, cooperators can spontaneously emerge by mutation.
Since the evolutionary dynamics are influenced by the definition of fitness, we
tested two commonly adopted fitness functions: accumulated payoff and average
payoff. Simulation results show that cooperation is strongly enhanced with the
accumulated payoff fitness compared to the average payoff fitness. However, the
difference between the two functions decreases as the average degree increases.
As the average degree increases, cooperation decreases with the accumulated
payoff fitness, while it increases with the average payoff fitness. Moreover,
with the average payoff fitness, low-degree nodes play a more important role in
spreading cooperative strategies compared to the case of the accumulated payoff
fitness.
