<p>We establish two long-term dynamic optimization differential game models between the government and industry based on grandfathering and benchmarking allocation methods of carbon emission allowance. Consequently, we derive the optimal trajectory of the carbon emission stock in the environment and the government and industry’s optimal strategic path evolutions over the long term. Through analysis, we discover that when external carbon allowances are provided, carbon emissions are lower under the benchmarking scenario than carbon emissions under the grandfathering allocation scenario. However, when the government acts as a leader, the optimal strategic paths for industry output and the optimal trajectory of carbon emission stock are consistent under both grandfathering and benchmarking allocation methods. Thus, a policymaker can combine the carbon emission stock target at the end of a certain period with the trajectory of carbon emission stock to deduce the carbon emission quotas allocated to different industries during that period and then deduce the optimal production strategies of industries in the corresponding period. Based on the equilibrium solution of the differential game, this research can serve as a theoretical reference for establishing the initial carbon emission quotas across different industries.</p> Graphical Abstract <p></p>