The paper considers the pricing problem of complementary products in a fuzzy dual-channel supply chain environment where there are two manufacturers and one retailer. Four different decision models are established to study this problem: the centralized decision model, MS-Bertrand model, RS-Bertrand model and Nash game model, where the consumer demand and manufacturing cost for each product are characterized as fuzzy variables. A closed form solution has been obtained for each model by using game theory and fuzzy theory. Numerical examples are presented to compare the maximal expected profits and optimal pricing decisions, and to provide additional managerial insights. The finding shows that the decision makers are more likely to choose industries with higher self-price elastic coefficient and lower complementarity in the retail channel to cooperate. We can obtain that consumers can benefit from the cooperation of the two manufacturers because of lower prices. We can also find that it might not be bad for retailer because it can expand demand and obtain more maximal expected profits.

This paper studies the multi-level supply chain network equilibrium optimization problem of multi-energy-efficiency products under different government subsidies and demand scales. In the equilibrium optimization problem, manufacturers determine the production volume of the energy-saving products; retailers decide the transaction volume with manufacturers, distribution volume for markets, and marketing efforts of energy-saving products; markets determine the transaction price. Firstly, the optimal decision-making behaviors of manufacturers, retailers, and markets are described. Simultaneously, the global optimization problem is transformed into a finite-dimensional variational inequality formulation. Then, the equilibrium conditions of the whole supply chain network are derived by the Euler method. Finally, a case study verifies the effectiveness of the proposed method. Interestingly, we found that energy-saving subsidies and demand scales were negatively correlated with the marketing efforts of the subsidized retailers for high energy-efficient products and positively correlated with the marketing efforts of non-subsidized retailers for high energy-efficient products in the same market; the development of retailers in the same market tended to be consistent, and the differentiation of the demand scale eliminated the retailers without a competitive advantage.