Study of game models and the complex dynamics of a low-carbon supply chain with an altruistic retailer under consumers’ low-carbon preference

This paper incorporates the retailer’s altruistic behavior into the low-carbon supply chain considering consumers’ low-carbon preference and establishes the Stackelberg game model and the vertical Nash game model from the perspectives of a static game and a dynamic game, respectively. First, the static analytical solutions of two models are obtained. Second, we explore the impacts of the retailer’s preference for altruism, consumers’ low-carbon preference and decision parameters on the complex nonlinear dynamic behaviors of the two models. The results show that the retailer’s altruistic behavior and consumers’ low-carbon preference narrow the stability region of the system. In the two game models, the retailer’s altruistic behavior always benefits the manufacture, but it is not good for the retailer; it is either beneficial to or not conducive for the whole supply chain. It is easier to make the system lose stability by accelerating the price adjustment parameter than by adjusting the carbon emission rate parameter. The higher adjustment parameter is even worse for the leader (the manufacturer) in the Stackelberg game, while in the vertical Nash game it is worse for the retailer. In addition, in the dynamic Stackelberg game, we are very surprised to find that a moderate consumer low-carbon preference is beneficial, but an excessive consumer low-carbon preference is not conducive to decision makers.