A jump–diffusion Stackelberg stochastic differential game in optimal carbon abatement strategies with green subsidy

The increasingly severe challenges of global warming necessitate a low-carbon transition that involves quantified estimation of carbon emission reduction policies. Carbon trading with abatement subsidization has proven to be an effective measure for evaluating the social cost of carbon emissions. However, conflicting targets between the government and firms can cause principal–agent issues in reducing carbon dioxide emissions. We propose a novel Itô–Lévy jump–diffusion state equation to depict the dramatic fluctuations of carbon prices, a critical factor in carbon trading. To analyze the complex game behaviors in carbon abatement, we construct a multiple players Stackelberg stochastic differential game model applying stochastic optimal control theory in principal–agent situations. Our model examines the incentive compatibility mechanism while considering the complex behaviors of carbon trading participants with asymmetric information. Optimal feedback control strategies are explicitly presented for the government and firms to achieve their separate targets of maximizing social welfare and production profits. Green subsidization coupled with carbon quotas trading is a viable option for promoting carbon abatement. However, high-carbon firms may attempt to deceive the government by pretending to be low-carbon ones. We illustrate that carbon traders with deceptive intentions lead to negative social welfare and hinder carbon abatement achievements.