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We introduce a differential game framework that retains tractability while not relying on commonly used restrictive linearity assumptions. Our frame is particularly suitable for analytical study the implication of a large set of heterogeneity traits across players. As an illustration, we employ it to derive new insights on climate-related policy. Our framework allows us to characterize emissions, consumption, and welfare across different equilibrium outcomes by comparing the Nash and Stackelberg equilibria of a game capturing climate negotiations between “global north” and a “global south.” We draw various comparisons between such outcomes and the efficient frontier. We find that both the global north and south underinvest in abatement. Stackelberg leadership by the global north reduces emissions and increases welfare over the Nash outcome, although emissions remain far from the optimum. Asymmetric vulnerability to climate change leads to a reversal in emissions, where the less vulnerable country emits more. We employ robust control to study how deep uncertainty affects outcomes.