Information asymmetry between the government and firms in the carbon market hinders firms from achieving sustainable emission reductions, thereby undermining carbon market efficiency and stability. This paper develops an intertemporal carbon market Stackelberg game model between the government and the firms. Scenarios of the benchmark, the carbon price floor adjustment, the carbon price ceiling adjustment, and the carbon price collars adjustment are constructed. The optimal carbon permit cap is then derived. The impacts of carbon price regulation on carbon market efficiency and stability are explored theoretically and numerically by analyzing a sample of 458 power plants in China’s national carbon market. The results reveal that carbon price regulation significantly affects carbon permit cap setting, market efficiency and stability. The carbon permit allocation ceiling and carbon price collars are critical factors influencing carbon market efficiency and stability. When the carbon permit allocation ceiling exceeds the carbon permit threshold floor, and the carbon price floor is greater than the benchmark carbon price threshold but lower than the carbon price threshold floor, carbon price floor and collars adjustments help raise the carbon price. However, these adjustments reduce carbon market stability and aggravate social carbon emission abatement costs. When the carbon permit allocation ceiling exceeds the carbon permit threshold ceiling and the carbon price ceiling is less than the benchmark carbon price threshold, both carbon price ceiling and collars adjustments help prevent a sharp rise in carbon price and increase market stability, but they do not decrease social carbon emission abatement costs. This paper provides theoretical support and policy implications for the construction of an intertemporal carbon market to ensure its effective and stable operation.