Optimal advertising decisions for promoting retail and online channels in a dynamic framework

Advertising plays an important role in sales promotion in supply chains. In this paper, advertising decisions for retail and online channels respectively, by retailer and manufacturer will be analyzed. The competition between retailer and manufacturer will be modeled by differential game theory, and feedback Nash equilibrium of the game will be obtained. Some insights are provided by using comparative statics. The obtained results show that compatibility factor of a product with online marketing, difference between manufacturer's online price and wholesale price, effectiveness of advertising, marginal profits, and cost of advertising all have significant effects on the advertising decisions in the equilibrium.