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With the robust control framework of Hansen and Sargent (2001), this paper investigates a stochastic differential game of transboundary pollution between two regions under Knightian uncertainty of stock dynamics. Both regions are assumed to play a noncooperative and a cooperative game, and the worst-case pollution accumulation processes for discrete robustness parameters are characterized. Our objective is to identify both regions’ optimal output and emission levels and analyze the effects of the Knightian uncertainty of pollution stock dynamics on both regions’ optimization behavior. We illustrate the results with some numerical examples.

A Stochastic Differential Game of Transboundary Pollution under Knightian Uncertainty of Stock Dynamics