["Journal of Public Economic Theory, Volume 28, Issue 4, August 2026. ", "\nABSTRACT\nWe study pure exchange economies with consumption externalities, where agents' preferences depend on others' consumption and may be non‐convex. Adopting a cooperative approach, we allow agents to form coalitions and introduce a notion of generalized fuzzy core. We show that core allocations can be decentralized via suitable price systems. We establish a core equivalence theorem for A‐equilibria, which generalizes Walras‐Nash and Berge equilibria with externalities. We also prove a corresponding equivalence result for economies with Arrowian markets, where generalized fuzzy core allocations can be supported as Information equilibria with personalized and market prices.\n"]