Emergence of Cooperation in Non-scale-free Networks

TL;DR

This paper introduces a payoff memory-based strategy updating rule demonstrating that random and small-world networks can foster cooperation better than scale-free networks, challenging previous assumptions about network heterogeneity and structure.

Contribution

It proposes a novel updating rule with payoff memory showing that non-scale-free networks can promote cooperation more effectively, questioning the role of heterogeneity and topology.

Findings

Random and small-world networks outperform scale-free networks in promoting cooperation.

Degree heterogeneity is neither necessary nor sufficient for cooperation.

Network topology alone does not determine cooperation levels.

Abstract

Evolutionary game theory is one of the key paradigms behind many scientific disciplines from science to engineering. Previous studies proposed a strategy updating mechanism, which successfully demonstrated that the scale-free network can provide a framework for the emergence of cooperation. Instead, individuals in random graphs and small-world networks do not favor cooperation under this updating rule. However, a recent empirical result shows the heterogeneous networks do not promote cooperation when humans play a Prisoner's Dilemma. In this paper, we propose a strategy updating rule with payoff memory. We observe that the random graphs and small-world networks can provide even better frameworks for cooperation than the scale-free networks in this scenario. Our observations suggest that the degree heterogeneity may be neither a sufficient condition nor a necessary condition for the widespread cooperation in complex networks. Also, the topological structures are not sufficed to determine the level of cooperation in complex networks.