A model of brand competition for durable goods supply chains in a dynamic framework

Game theory is an efficient tool to represent and conceptualize the problems concerning conflict and competition. In recent years and especially for durable products, competition between domestic and foreign brands for gaining market share has received a considerable attention. This paper study electronic commerce concepts by differential game theory and introduce a novel and comprehensive model for analyzing dynamic durable goods supply chains. Manufacturer of domestic brand as leader of the game announces his wholesale price to his retailer. Then the exclusive retailers of domestic and foreign brands play a Nash differential game in choosing their optimal retail prices and advertising efforts over time. Moreover, online pricing and advertising in a direct sales channel constitute other control variables of the manufacturer. Feedback equilibrium policies for the manufacturer and the retailers are obtained by assuming a linear demand function. A case study and sensitivity analysis are carried out to provide numerical results and managerial insights. We found that there is a reverse relationship between price sensitivity of demand and optimal levels of price and advertising efforts. Increase in advertising effectiveness parameter leads to enhancement of advertising efforts in relative marketing channel, but does not have a significant effect on pricing decisions.