Carbon allowance trading by power generation enterprises, facilitated through both internal and external markets, is a crucial mechanism for harmonizing carbon allowances in accordance with trading policies. Various trading pathways significantly affect these enterprises' decisions to reduce emissions. This paper examines the carbon emission reduction decisions of participants in the Chinese power generation industry under varying carbon allowance trading pathways. The Stackelberg game model is employed to analyze the challenges faced by the power generation industry in reducing carbon emissions, which comprises larger firms with a larger installed capacity and smaller power generation companies. The research indicates that: (1) when considering external carbon trading exclusively, variations in carbon abatement cost coefficients allow the two parties to adopt substitutable roles to mitigate supply shortages in the market; (2) when internal and external carbon trading paths coexist, they can effectively buffer external market shocks and curb large profit fluctuations, and (3) carbon trading price volatility and allowance sufficiency significantly affect the economic outcomes of power firms. Carbon trading prices determine corporate profits, while the scarcity of allowances affects firms' marginal decisions more indirectly. A smaller installed capacity is more vulnerable to external price volatility and institutional constraints. (4) The adjustment of carbon allowance allocation significantly moderates the behavior of power producers. Under allowance scarcity and high abatement costs, high cost subjects take the initiative to withdraw from the market. In contrast, low-cost subjects benefit from carbon allowance trading or market pricing, resulting in the redistribution of resources and profits.
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