ABSTRACT Managing a multi-agent supply chain within a hybrid carbon trading framework, which integrates Certified Emission Reductions (CERs) and Carbon Quota Trading (CQT), presents a significant challenge. This complexity is further amplified by the interplay of competition and cooperation among agents. Motivated by this, we develop a biform game-based cooperative mechanism for a two-stage supply chain that includes a high-emission manufacturer, a negative-emission manufacture and a downstream retailer. This mechanism is designed to encapsulate both the non-cooperative and cooperative game elements. The former features a product competition game among the manufacturers and retailer, setting the stage for the cooperative game without directly yielding equilibrium solutions. The latter involves a cost-sharing agreement for the CER project's initial investment, informed by various coalitional zero-sum games. Our analytical findings, corroborated by numerical simulations, reveal that the biform game coordination mechanism significantly enhances the volume of CERs traded and consumer surplus, compared to a non-cooperative scenario. It effectively aligns the collaborative efforts of all agents within the supply chain. This research contributes substantially to the literature on coordinating multi-stage, multi-agent supply chains, and the strategic deployment of emission reduction initiatives in supply chains. It also offers valuable managerial insights for the design of government regulations in carbon markets.