Group-size dependent synergy in heterogeneous populations

TL;DR

This paper investigates how varying group sizes and synergy factors influence cooperation levels in public goods games, revealing that larger groups with size-dependent synergy generally promote higher cooperation.

Contribution

Introduces a model with size-dependent synergy factors in heterogeneous populations, showing how group size influences cooperation dynamics and community benefits.

Findings

Larger groups with increasing synergy promote higher cooperation.

Smaller groups perform better with homogeneous synergy.

Heterogeneous topologies exhibit similar qualitative behavior.

Abstract

When people collaborate, they expect more in return than a simple sum of their efforts. This observation is at the heart of the so-called public goods game, where the participants' contributions are multiplied by an $r$ synergy factor before they are distributed among group members. However, a larger group could be more effective, which can be described by a larger synergy factor. To elaborate on the possible consequences, in this study, we introduce a model where the population has different sizes of groups, and the applied synergy factor depends on the size of the group. We examine different options when the increment of $r$ is linear, slow, or sudden, but in all cases, the cooperation level is higher than that in a population where the homogeneous $r$ factor is used. In the latter case, smaller groups perform better; however, this behavior is reversed when synergy increases for larger groups. Hence, the entire community benefits because larger groups are rewarded better. Notably, a similar qualitative behavior can be observed for other heterogeneous topologies, including scale-free interaction graphs.