The evolution of cooperation in a mobile population on random networks: Network topology matters only for low-degree networks

TL;DR

This study investigates how network topology influences the evolution of cooperation among mobile individuals, revealing that topology matters mainly for networks with low average degrees, while high-degree networks behave similarly to complete graphs.

Contribution

It extends existing models to various random networks, showing that network effects diminish as average degree increases, with a specific threshold depending on network properties.

Findings

Network topology impacts cooperation only in low-degree networks.

High-degree networks exhibit similar cooperation levels to complete graphs.

Threshold degree for topology effects varies with network characteristics.

Abstract

We consider a finite structured population of mobile individuals that strategically explore a network using a Markov movement model and interact with each other via a public goods game. We extend the model of Erovenko et al. (2019) from complete, circle, and star graphs to various random networks to further investigate the effect of network topology on the evolution of cooperation. We discover that the network topology affects the outcomes of the evolutionary process only for networks of small average degree. Once the degree becomes sufficiently high, the outcomes match those for the complete graph. The actual value of the degree when this happens is much smaller than that of the complete graph, and the threshold value depends on other network characteristics.