To achieve the goals of carbon peak and carbon neutrality, the low-carbon transformation (LCT) of high-carbon firms is inevitable. We construct game models of a supply chain with different dominant types under a mixed carbon policy that embraces carbon cap-and-trade and carbon tax. Solving each dominant model, we derive the effective area and optimal threshold of the mixed carbon policy to guide LCT. We find that the selling price, market demand, and profit of the supply chain system are equal in different dominant models due to the mixed carbon policy, but when a company dominates the supply chain, its profit is higher than when it is a subordinate. In addition, the high-carbon manufacturers (HCM) will pursue LCT only when the sum of the carbon tax rates and carbon trading prices is within a certain threshold, and the subordinate HCM are more likely to be driven to pursue LCT. Therefore, the government should adopt a differentiated hybrid carbon policy, setting a high (low) carbon tax rate for the HCM in a dominant (subordinate) position.
