Emergence of contagious cooperation in community-structured networks

Multilevel sociality, in which large communities emerge from interconnected subgroups, is a hallmark of primate societies and a central focus of the social brain hypothesis. We investigate whether such organizational forms can, on their own, foster cooperation when defection is individually optimal and the population is initially dominated by defectors. Using the spatial Prisoner's Dilemma on community-structured networks, we derive analytical conditions under which cooperation, once present, spreads contagiously across communities without altering payoffs or invoking external enforcement. The mechanism arises from intercommunity interactions, which facilitate cross-community transmission and buffer against isolated defections. We further show that larger groups within overlapping communities expand the parameter region supporting propagation. The effect extends to Stag Hunt and Snowdrift games, indicating robustness across incentive structures. While our analytical results rely on deterministic unconditional imitation, extensive numerical simulations demonstrate that the spread of cooperation is robust to stochastic perturbations, revealing that behavioral inertia can counterintuitively stabilize cooperation within small community structures. We also evaluate our framework on a real-world coauthorship network, showing that the emergence of contagious cooperation in community-structured networks is not only present in theoretical networks but also in empirical architectures. Our contributions are to establish sufficient conditions for contagious cooperation within the considered class of networks and dynamics, quantify how overlap and group size determine the propagation threshold, and establish community architecture as a principal determinant of cooperative dynamics in social, economic, and biological systems, showing that, in the right network architecture, cooperation can arise and persist without external support.