Pricing game of two substitutable products supply chains under centralized and decentralized decisions

This article considers the pricing game of two supply chains which compete in the market with two substitutable products in a fuzzy environment. The two substitutable products supply chains are either centralized, i.e. manufacturers sell their own products, or they are decentralized where manufacturers sell their products to the market through retailers. By using game and fuzzy set theories, two pricing game models are established and the corresponding optimal pricing strategies in closed form are also given. At last, some managerial analyses are given by numerical approach.