Evolutionary games on networks with negative edge-based environmental feedback

In strong-selection evolutionary games on networks with edge-specific binary environmental states, negative feedback linked to cooperation versus defection yields bistability and Hopf-driven oscillations in well-mixed populations.

• Why it matters: Environmental feedback can reshape payoff structures for cooperation, but how such feedback-evolving games behave with population structure under non-weak selection is not well resolved.
• What they did: The study analyzes an edge-environment game using mean-field and pair approximation (tracking strategy pairs plus edge states) and agent-based simulations under strong selection.
• The result: Sparse networks (low node degrees) remove bistability, suppress oscillations, and stabilize intermediate cooperation levels, with pair approximation matching simulations better on sparse graphs.

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