Evolutionary dynamics of public goods games on random hypergraphs with environmental feedbacks

Understanding how environmental feedbacks and higher-order interactions jointly shape the evolution of cooperation remains profoundly underexplored. To bridge this gap, we introduce a coevolutionary model of public goods games with environment on random hypergraphs. Individuals interact within subgroups, and their payoffs are dynamically modulated by an environmental state reflecting collective resource consumption. Crucially, this environmental state itself evolves in response to the population’s strategic composition, creating a tight bidirectional feedback loop. Combining analytical replicator dynamics with numerical simulations, we systematically analyze how cooperation emerges and stabilizes under variations in group size (g), synergy factor (R), initial environmental state (n0), and learning uncertainty (κ). Key findings demonstrate that larger group sizes (g) and stronger synergy factors (R) significantly enhance cooperation. Paradoxically, initially degraded environments (low n0) promote cooperation by punishing defectors, while initially favorable environments (high n0) can also catalyze cooperation in the long run due to the environmental feedback loop. Notably, high stochasticity in decision-making (large κ) disrupts the strategy–environment coupling, undermining cooperation even under favorable synergy factor. These results underscore the indispensable role of integrating higher-order interaction structures with eco-evolutionary feedback loops for understanding collective action, offering novel theoretical insights for designing robust cooperation mechanisms in environmentally constrained systems.