Product and price competition with selection of unique and common features and different quality levels

Abstract

Firms must determine the best features and prices for their new products to be competitive in the market. We consider product features that are discrete and can have different quality levels. We formulate and solve the two competing firms’ new product introduction and pricing problems, in which both firms introduce their products sequentially. We differentiate unique features that are present only in one product and common features that are shared between two products. The firms’ new product introduction problem is formulated as a mixed-integer nonlinear program, and the firms’ pricing problem is formulated as a nonlinear program. These formulations allow a firm to determine the optimal features and the price in a competitive setting with general product value and cost functions. For linear product value and cost functions and a demand function linear in price but nonlinear in the number of features or the feature quality level selected, we analytically determine the firms’ optimal feature and quality level selection in anticipation of the features and the quality levels of the competitor’s product and the resulting equilibrium prices. The optimal selection of unique features depends only on the value and cost of that feature’s quality levels and the firms’ price sensitivities. A firm with a competitive advantage tends to include more features or high-quality feature levels in its products; otherwise, it differentiates its product via feature selection to lessen the substitution effects of common features. We identify cases where, despite the firms being symmetric other than their entry order, the leader’s optimal feature selection is introducing a product with fewer or lower quality features compared to the second firm. Despite this, the leader still obtains a higher profit than the second firm.