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.

翻译：通过成对相互作用理解社交网络中合作的涌现已取得进展，但针对基于群体的公共物品博弈（PGGs）的相应理论仍较少被探索。本文提出了在任意群体结构上公共物品博弈中合作行为蓬勃发展的理论条件，这些条件在弱选择假设下具有精确性。我们发现，一类原本无法产生合作的网络（如星形图）在公共物品博弈中特别有利于合作的形成。更普遍而言，公共物品博弈几乎能在所有网络类型中支持合作，且该结论对各类模型细节具有鲁棒性。公共物品博弈的这一根本优势源于通过群体分离实现的自我互惠机制，以及通过二阶相互作用形成的聚类效应。我们还将公共物品博弈应用于实证网络，结果表明公共物品博弈可能成为现实世界系统中合作涌现的一种具有前景的相互作用模式。