Evolution of cooperation in multilevel public goods games with community structures

TL;DR

This paper presents an analytical study of how cooperation evolves in multilevel public goods games within community-structured populations, revealing conditions that favor cooperation or defection based on imitation strengths.

Contribution

It introduces a minimalist evolutionary model for multilevel public goods games and analyzes the effects of imitation strength within and between communities on cooperation.

Findings

Weak within-community imitation promotes cooperation.

Strong between-community imitation enhances cooperation.

Strong imitation both within and between communities leads to defection dominance.

Abstract

In a community-structured population, public goods games (PGG) occur both within and between communities. Such type of PGG is referred as multilevel public goods games (MPGG). We propose a minimalist evolutionary model of the MPGG and analytically study the evolution of cooperation. We demonstrate that in the case of sufficiently large community size and community number, if the imitation strength within community is weak, i.e., an individual imitates another one in the same community almost randomly, cooperation as well as punishment are more abundant than defection in the long run; if the imitation strength between communities is strong, i.e., the more successful strategy in two individuals from distinct communities is always imitated, cooperation and punishment are also more abundant. However, when both of the two imitation intensities are strong, defection becomes the most abundant strategy in the population. Our model provides insight into the investigation of the large-scale cooperation in public social dilemma among contemporary communities.