Public goods games on any population structure

TL;DR

This paper develops a theoretical framework for understanding how cooperation can emerge in public goods games across various population structures, highlighting the robustness of PGGs in promoting cooperation even in complex networks.

Contribution

It provides the first comprehensive theoretical conditions for cooperation in PGGs on arbitrary networks, including empirical networks, under weak selection.

Findings

Star graphs can promote cooperation in PGGs.

PGGs support cooperation on most networks regardless of model details.

Empirical network analysis shows PGGs' potential in real-world cooperation emergence.

Abstract

Understanding the emergence of cooperation in social networks has advanced through pairwise interactions, but the corresponding theory for group-based public goods games (PGGs) remains less explored. Here, we provide theoretical conditions under which cooperation thrives in PGGs on arbitrary population structures, which are accurate under weak selection. We find that a class of networks that would otherwise fail to produce cooperation, such as star graphs, are particularly conducive to cooperation in PGGs. More generally, PGGs can support cooperation on almost all networks, which is robust across all kinds of model details. This fundamental advantage of PGGs derives from self-reciprocity realized by group separations and from clustering through second-order interactions. We also apply PGGs to empirical networks, which shows that PGGs could be a promising interaction mode for the emergence of cooperation in real-world systems.