To achieve SDGs (sustainable development goals) and carbon neutrality goals, the Chinese government have been adopting the cap-and-trade regulation to curb carbon emissions. With this background, members in the supply chain should properly arrange their carbon reduction and marketing decisions to acquire optimal profits, especially when the favorable event may happen, which tends to elevate goodwill and the market demand. However, the event may not be of their benefit when the cap-and-trade regulation is conducted, since the increase in market demand is always associated with an increase in carbon emissions. Hence, questions arise about how the members adjust their carbon reduction and marketing decisions while envisioning the favorable event under the cap-and-trade regulation. Given the fact that the event occurs randomly during the planning period, we use the Markov random process to depict the event and use differential game methodology to dynamically study this issue. After solving and analyzing the model, we acquire the following conclusions: (1) the occurrence of the favorable event splits the whole planning period into two regimes and the supply chain members should make optimal decisions in each regime to maximize the overall profits. (2) The potential favorable event will elevate the marketing and carbon reduction efforts, as well as the goodwill level before the event. (3) If the unit emissions value is relatively low, the favorable event will help to decrease the emissions quantity. However, if the unit emissions value is relatively large, then the favorable event will help to increase the emissions quantity.
Keywords: cap-and-trade regulation; carbon reduction; differential game; marketing; random stopping time optimal control; supply chain management.