Biform differential game approach to dynamic carbon reduction cooperation in transnational supply chains under CBAM

The Carbon Border Adjustment Mechanism (CBAM) is a border tax implemented by highly carbon-regulation countries (HCRC) on imports from less carbon-regulation countries (LCRC). To analyse carbon reduction cooperation in transnational supply chains under CBAM, this study develops a biform differential game model involving a distributor in HCRC and two manufacturers (from HCRC and LCRC) supplying homogeneous products. Within this framework, supply chain members cooperate in carbon reduction while independently setting the wholesale prices or retail prices. The findings reveal a key distinction between cooperative and non-cooperative modes: under non-cooperation, pricing and emission reduction decisions remain static, whereas under cooperation, they dynamically evolve and gradually stabilise. Moreover, as the CBAM price increases, distributors in the cooperative model increase the LCRC product sales but reduce them in the non-cooperative setting. Consequently, under cooperation, the distributor’s profit increases with CBAM prices, while under non-cooperation, the profit follows an inverse U-shaped pattern. Finally, the cooperative mechanism enhances sales, emission reductions, and both LCRC and HCRC manufacturers’ profits compared to the non-cooperative model. However, the distributor achieves higher profits only when CBAM prices are sufficiently high, and thus should adopt the cooperative strategy under the same condition.