Network reciprocity reshaped by environmental knowledge and feedback

Cooperative interactions often unfold in environments that are shaped by collective behavior, yet how knowledge about such changing environments feeds back into evolutionary dynamics remains poorly understood. While network reciprocity explains how spatial structure enables clusters of cooperators to emerge and grow under certain conditions, it typically ignores how individuals respond to environmental change. Here, we integrate stochastic environmental feedback with network reciprocity to examine how knowledge about environmental state shapes the evolution of cooperation in structured populations. We compare regimes in which individuals either condition their behavior on the current state or remain unaware of it. Under weak selection, we derive a simple condition showing that cooperation is favored when the benefit-to-cost ratio exceeds a modified classic reciprocity threshold accounting for the effect of environmental transitions and state knowledge. Environmental shifts can either promote or hinder cooperation depending on accessibility and fidelity of state knowledge. Counterintuitively, greater knowledge does not universally enhance cooperation: for certain transition rules, state awareness raises the critical threshold for cooperation, a phenomenon we term a "knowledge curse". Our results reveal that, in an ever-changing environment, cooperation in structured populations emerges from a subtle interplay between environmental feedback and information availability.