The carbon quota allocation rules of China's pilot carbon emissions trading (CET) regions are various, which mainly include benchmarking, historical carbon intensity reduction and auctioning. When the allocation rules change, it is unresolved how to achieve the optimal product prices and effectively allocate the carbon emissions reduction profits of CET-covered enterprises in the cooperative supply chain. Thus, this paper uses the Stackelberg game, Nash equilibrium and the Shapley value based on cost modification to investigate these issues. The results indicate that: (1) The increasing carbon prices can always improve the retail prices only under the auctioning rule. Meanwhile, the growing low-carbon awareness of consumer cannot be always conducive to improving the wholesale and retail prices, and the similar product prices of non-CET-covered enterprises have greater impact on the wholesale prices than that on the retail prices. (2) Only under the free carbon quota allocation rules, can the optimal wholesale and retail prices under the Stackelberg game be always higher than those under the Nash equilibrium. Meanwhile, the auctioning rule can better reduce carbon emissions than the free allocation rules. (3) Improving carbon emissions reduction contribution and emission reduction costs can be conducive to increasing the carbon emission reduction profits of the supplier and retailer, while the impact of carbon emission reduction contribution on improving the carbon emission reduction profits is not always greater than that of the carbon emission reduction costs. [ABSTRACT FROM AUTHOR]