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Against the backdrop of cap-and-trade regulations, we construct a low-carbon supply chain in which a seller holds the manufacturer's equity. We investigate the impact of the seller's equity holding and the cap-and-trade regulations on the supply chain members' optimal decisions, profits and coordination in the cases of information symmetry and asymmetry. We find that, regardless of whether there is information asymmetry or symmetry, the manufacturer always benefits from an equity holding, while the seller can only earn higher profits through equity holding if the percentage of equity holding and the level of consumer low-carbon awareness are both sufficiently high. Both the seller and the manufacturer prefer the information asymmetry scenario when the manufacturer's efficiency in emission reduction is below a particular threshold. In addition, equity holding can incentivize the manufacturer to share its information with the seller. Equity holding is beneficial for emission reduction and market demand but is not always beneficial for improving the supply chain's total profit and reducing the supply chain's total carbon emissions. Finally, with a transfer payment contract, a decentralized supply chain can obtain the same optimal profits as in the centralized supply chain scenario, and both the manufacturer and seller can earn higher profits than before. [ABSTRACT FROM AUTHOR]

The relation between longitudinal emission reduction investment of supply chain enterprises and the government's subsidy policy is studied in this paper, the game model against subsidy of the government for emission reduction investment of manufacture and retailer is developed. This study analyzes the optimal investment of enterprises and the optimal emission reduction subsidy of the government under the Nash and Stackelberg game conditions. The results show that the government's emission reduction subsidies for two parties on the supply chain, as well as the benefits to such two parties, are affected by the cooperative relationship in the supply chain. That is, manufacturer and retailer are in the highest position in the Nash game, followed by the Stackelberg game and the lowest in central decisions. Comparing the subsidy differences of the government in the emission reduction investment by manufacturer and retailer under different force structures, the longitudinal emission reduction investment in the supply chain and the government's subsidy policy under different game conditions are concluded. [ABSTRACT FROM AUTHOR]