Piece-Wise Constant Pricing in Dynamic Marketing

Usually in dynamic marketing, economic agents (producer, retailer, etc.) often use various types of communications (promotion, advertising, incentives, etc.) and discounts. We study pricing in a dynamic marketing model. In contrast to the classical formulations, we are studying a more economically adequate case of piece-wise constant pricing. Thus, we consider the profit of the manufacturer as the function of wholesale discount levels, while the profit of the retailer is considered as the function of retail discount levels. Earlier, we get (under rather realistic assumptions) the strict concavity of these profits. This allows us to move on to the next stage of research: to study the equilibria. However, the equilibria cannot always be calculated explicitly, i.e., in closed form, since it is required to solve systems of nonlinear algebraic equations. The result is that if the wholesale discount is constant and the retail discount is piece-wise constant, then the Stackelberg equilibrium under the leadership of the manufacturer can be calculated in closed form.