Optimising government’s policy and heterogeneous firms’ strategies under an emissions trading system: a bi-level game-theoretic approach

As emission trading systems (ETS) are increasingly adopted worldwide, understanding strategic interactions between governments and firms is crucial for effective policy design. This paper develops a bi-level Stackelberg game model to optimise ETS performance. At the upper level, the government sets the emission reduction target to maximise social welfare; at the lower level, firms with heterogeneous emission intensity optimise operational decisions under price competition, with an endogenous carbon price mechanism capturing market equilibrium. We transform this bi-level model into a single-level Mixed-Integer Quadratic Programming (MIQP) problem and prove the existence and uniqueness of the Stackelberg equilibrium. Using this model, we analyse how industrial competition and consumer environmental awareness (CEA) affect ETS outcomes. Results reveal that ETS creates differentiated impacts: carbon-intensive firms face greater operational adjustments, while carbon-efficient firms gain competitive advantages and higher profits. Competitive industries exhibit lower carbon prices, greater emission reductions, and higher trading volumes than monopoly industries, and appropriate targets can improve both social welfare and firm profitability. Rising CEA leads to stricter targets and enhances social welfare, but excessive CEA undermines profitability, particularly for carbon-intensive firms in highly competitive industries. These findings guide policymakers in designing ETS that balance emission reduction, economic development, and consumer welfare.