This paper outlines an approach to modelling strategic behaviour in the Global Trade Analysis Project’s computable general equilibrium model GTAP-E. This modelling innovation has been motivated by the desire to compute game-theoretic equilibria for climate policy analysis to gain insights into the potential outcomes of international climate change negotiations and optimal burden sharing arrangements. Demonstrations of the model applied under a permit trading regime and independent carbon taxation are given. The demonstrations show that, for the same value placed on emissions abatement, an international permit trading scheme results in a higher payoff for all regions. We also find that, for the same level of abatement, optimal differential carbon taxes lead to a significantly lower total welfare loss than uniform taxes imposed under international permit trading, due to pre-existing taxes. The technique can be applied more broadly to any numerical optimization of GEMPACK models.