Coordination and price competition in a duopoly common retailer supply chain

This paper analyzes the coordination and competition issues in a two‐stage supply‐chain distribution system where two vendors compete to sell differentiated products through a common retailer in the same market. The demand of a product not only depends on its own price, but also on the price of the other. Mathematical models have been developed to analyze the coordination issues under three different contexts: (i) price competition without channel coordination; (ii) price competition with channel coordination; and (iii) global coordination. It has been shown that under certain conditions, price competition through the dynamic process of price adjustment reaches the Nash–Bertrand equilibrium. Conditions have been derived for the Nash–Bertrand equilibrium to be dynamically stable. Further, it has been shown that duopoly competition can make consumers better‐off or worse‐off depending on the degree of product differentiation and the type of the product; while coordination enhances overall supply‐chain profitability. The model is illustrated with suitable numerical examples.