When Does Clustering Matter Again? Hypergraph and Weighted-Edge Corrections to Network Reciprocity under Environmental Feedback

Extend evolutionary games on networks to (i) weighted edges capturing interaction intensity, and (ii) hypergraph interactions capturing public-goods synergies; couple these with local environmental feedback defined on edges/hyperedges. Systematically measure how clustering, motif frequencies, and degree variance shape the dominance condition for cooperation across update rules. This tests whether the “clustering doesn’t matter” finding is contingent on pairwise additivity and fixed payoffs by introducing hyperedges and edge-level eco-feedback, which can make triadic closure amplify cooperative spillovers. It builds on update-rule sensitivities and micro-rule non-equivalence issues to identify under which combinations of update rule and higher-order/weighted structure clustering regains predictive power. A positive result would reconcile conflicting findings about clustering’s role and clarify when simple network summaries fail, improving design principles for microbial consortia and social dilemmas with local resources.

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