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Analysis on Retailer-Stackelberg Process' Stability in Two-Echelon Supply-Chain with Different Demand Curves

In the two-echelon supply-chain literature, the optimal prices and optimal profits of the manufacturer and the retailer should be affected by both of the relationship between them and the shape of the demand curve. As a common type of two-echelon supply-chain process, the retailer-Stackelberg process has a retailer for Stackelberg leader and a manufacturer for Stackelberg follower. In this paper, we will discuss the influence to the optimal prices and profits by changing the parameters in demand curve, and analyze the stability of the optimal prices and profits of the manufacturer and the retailer with three different demand curves by using the Lipschitz properties.