A competitive dynamic pricing model when demand is interdependent over time

In this study, we contribute to the dynamic pricing literature by developing a finite horizon model for two firms offering substitutable and nonperishable products with different quality levels. Customers can purchase and store the products, even if they do not need them at the time, in order to use them in future. The stockpile of the products generated by customers affects the demand in future periods. Therefore, the demand for each product not only is a function of prices and quality levels, but also of the products' stockpile levels. In addition, the stockpile levels change the customers' consumption behavior; more product in a stockpile leads to more consumption. Therefore, we address not only the price and demand relationship but also the stockpiling and consumption relationship in a competitive environment. The decision variable of each firm at the beginning of each period is its unit sale price. We use a deterministic dynamic program to calculate the equilibrium prices at the beginning of each period. By assuming that the market stockpile is public information, we show the existence of a unique Nash equilibrium. We next consider the case when the firms do not know the market stockpile. We then develop appropriate heuristics to calculate the optimal prices in each case. A numerical study is also provided to calculate the price levels in different scenarios and compare their performances.