Game Theoretic Models on Product Differentiation

Abstract

Positioning and pricing of products are two very crucial decisions that a company needs to make in a competitive market. These decisions are in turn affected by a variety of factors, which include the intensity of competition; consumer demand; consumer behavior; and type of competing firms (incumbent or entrant; national brand or store brand). We, therefore, study product positioning/differentiation and pricing decisions of competing firms under three different settings described by different combinations of these factors. We use extensions of Hotelling's framework for horizontal product differentiation to model the three different settings, which are solved as multistage games using the concept of Sub-game Perfect Nash Equilibrium (SPNE). The first setting studies a duopoly market consisting of one national brand manufacturer and a retailer. The national brand manufacturer sells its product to the consumers through the retailer. The retailer also sells its own store brand, which is horizontally differentiated from the national brand. This study presents the following important insights: (i) firms differentiate less with the increase in retailer's margin on national brand; (ii) both the firms stand to lose while consumers benefit from any increases in the retailer's margin on the national brand. The second setting models the product differentiation for an entrant and incumbent firm in the presence of variety seeking consumers. We find that entrant differentiates less from the incumbent firm for markets with lower fractions of variety seekers, but differentiates more if higher fraction of variety seeking consumers is present in the market. Also, it is interesting to note that profits for the two firms initially decrease and then increase with increasing variety seeking fraction. Finally, the third setting models the competition between two symmetric firms based on delivery time in addition to product differentiation and pricing. This makes the model more interesting to study although more challenging to solve. The model turns out to be mathematically intractable. This is an ongoing research and we present certain directions for future research.