In view of the problems of asymmetric information, high operating costs, low management efficiency, and difficult supervision in the carbon trading system, applying blockchain technology to the carbon trading market is conducive to sharing information among manufacturers with different emission reduction efficiencies, and promoting manufacturers' cooperation to improve emission reduction level. This paper uses the cooperative game method to study the cooperation between two competing manufacturers in a low-carbon supply chain based on blockchain technology, and obtains the optimal production strategy, emission reduction strategy, and profit distribution of manufacturers after cooperation under the cooperative situation. A comparative analysis is conducted with traditional competitive emission reduction models. The impact of blockchain costs, emission reduction efficiency and degree of competition on optimal decision-making and social welfare was further discussed. The results show that: 1) Through the sharing of emission reduction information on the blockchain carbon trading platform, carbon trading efficiency is improved. However, higher blockchain operating costs will reduce the willingness of manufacturers to enter the platform; Manufacturers' production decreases as emission reduction efficiency of their competitors increases, and increases as their own emission reduction efficiency increases; An increase in degree of competition will lead to a decline in manufacturers' profits and social welfare, as well as a reduction in carbon emissions. In addition, higher carbon prices are conducive to reducing carbon emissions and improving social welfare. 2) In the cooperative situation, when the transfer agreement price is at a certain threshold, it is profitable for both manufacturers to conduct carbon emission quota transactions in the form of transfer agreement. Otherwise, as the transfer agreement price changes, it will harm the profits of a certain manufacturer. 3) Compared to competitive situations, cooperation between competing manufacturers based on the blockchain carbon trading platform can achieve higher returns while generating lower carbon emissions. Therefore, from both environmental and economic perspectives, cooperation is a win-win strategy for both environment and manufacturers.