Invasion of Cooperation in Scale-Free Networks: Accumulated versus Average Payoffs

Genki Ichinose*, Hiroki Sayama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


It is well known that cooperation cannot be an evolutionarily 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 on 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 for the accumulated payoff fitness, while it increases for the average payoff fitness. Moreover, for the average payoff fitness, low-degree nodes play a more important role in spreading cooperative strategies than for the accumulated payoff fitness.

Original languageEnglish
Pages (from-to)25-33
Number of pages9
JournalArtificial Life
Issue number1
Publication statusPublished - 2017 Feb 1
Externally publishedYes


  • Evolution of cooperation
  • Evolutionary game
  • Fitness function
  • Invasion dynamics
  • Prisoner's dilemma
  • Scale-free network

ASJC Scopus subject areas

  • Biochemistry, Genetics and Molecular Biology(all)
  • Artificial Intelligence


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