Emergence of cooperation in nonlinear higher-order public goods games
Phys. Rev. E 114, 034316 – Published 29 September, 2026
DOI: https://doi.org/10.1103/54zg-75zk
Abstract
Evolutionary game theory has provided substantial contributions to explain the emergence of cooperation under unfavorable conditions in ecology, economics, and the social sciences. Recently, inspired by newly available empirical evidence on group interactions, higher-order networks have emerged as a natural framework to encode multiplayer games in structured populations. Here we study the emergence of cooperation in nonlinear public goods games on hypergraphs, where collective reinforcement captures the synergistic or discounting effect associated with each additional cooperator. In well-mixed populations, when all games have the same number of players, the system displays a transition whose nature changes from continuous to discontinuous depending on the form of nonlinearity. By contrast, when games involving different numbers of players coexist, an additional bistability region between an active coexistence state and full cooperation may emerge. We further find that scale-free hypergraphs promote cooperation, highlighting the crucial role played by both the initial placement of cooperators and the presence of hyperdegree correlations. Overall, our results provide a comprehensive characterization of nonlinear public goods games on hypergraphs and open avenues for richer models of evolutionary dynamics of multiplayer games on structured populations.
