This study develops a cooperative game-theoretic framework for financing global public goods in an economy with asymmetric member states and applies it to the case of United Nations funding. The analysis examines whether a personalized-pricing contribution structure can improve upon an empirically grounded non-cooperative benchmark derived from observed member-state contribution patterns. Moving from a Nash-equilibrium benchmark in which states act primarily in self-interest to a cooperative model, the proposed approach aligns each country's financial contributions with the benefits it derives from United Nations activities. Using agent-based simulations calibrated to United Nations contribution data, this paper compares the benchmark allocation with the cooperative Trading equilibrium and shows that the proposed framework increases global utility, reduces free riding, and improves the efficiency of resource allocation. The findings suggest that this framework can serve as a normative benchmark for a more equitable financing arrangement for global public goods in the United Nations context. Further research is needed to evaluate the institutional and political feasibility of implementing such a model in practice.