Invasion of cooperation in scale-free networks: Accumulated vs. average payoffs

TL;DR

This study investigates how different fitness definitions influence the invasion and spread of cooperation in scale-free networks, revealing that accumulated payoffs strongly promote cooperation, especially among high-degree nodes, with effects varying by network connectivity.

Contribution

It compares accumulated versus average payoff fitness functions in the evolution of cooperation on scale-free networks, highlighting their distinct impacts on invasion dynamics and the role of node degree.

Findings

Cooperation is more strongly promoted by accumulated payoff fitness.

The difference between fitness functions diminishes as average degree increases.

Low-degree nodes are more influential in spreading cooperation under average payoff fitness.

Abstract

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.