تبعیض قیمت ناقص در مدل تفکیک عمودی

We explore the competitive implications of third-degree price discrimination based on consumer information of varying degrees of “precision” in a vertical differentiation duopoly model. We show that, if the cost of information is below a threshold, only the high quality firm will acquire it and offer targeted promotions, while the low quality firm will commit to a uniform price, for any degree of consumer information precision. Equilibrium profits of the high quality firm are monotonically increasing and that of the low quality firm monotonically decreasing as a function of the consumer information precision. Finally, social and consumer welfare are monotonically increasing with respect to the precision of consumer information.

The rapid development of the Internet as a medium of communication and commerce has prompted many marketers and retailers to accumulate a large amount of customer-specific information. Firms analyze the available information with the aid of sophisticated software tools and segment their customers according to certain verifiable characteristics such as age, income, place of residence, browsing patterns and past purchasing behavior. Consumer segmentation, in turn, helps firms tailor their promotional strategies, depending upon each group's preferences for a firm's brand. For example, different segments can receive a different quality of service or different discounts.2 How refined customer segmentation is, depends critically on the quality and quantity of customer-specific information that a firm has acquired. The continuing growth of information technology (IT) has clearly had a positive impact on the ability of customer databases to predict consumer preferences more accurately. We formulate a model of oligopolistic third-degree price discrimination with one high and one low quality firm (vertical differentiation). Consumer information partitions the characteristics space, allowing firms to classify the consumers into different segments by imperfectly estimating the brand premium each consumer is willing to pay for the high quality product. Firms can then tailor their prices to each consumer segment. Higher information precision is modeled as a refinement of the partition. We address the following questions: (i) Does the high quality firm have the stronger incentive to acquire information and price discriminate? (ii) How does the precision of the available information affect product quality? (iii) How do firms' incentives for information acquisition, profits and welfare evolve as information precision improves? The literature on oligopolistic third-degree price discrimination in location models can be roughly divided into two strands.3 The first strand assumes symmetric firms with the ability to segment consumers either into two groups or perfectly.4 A common thread in those papers is that profits under price discrimination fall short of those under a uniform pricing rule. The second strand deals with asymmetric firms but maintains the assumption that firms can classify the consumers either into two groups or perfectly.5 Corts shows that in a duopoly model of vertical differentiation, price discrimination between two groups of consumers leads to lower profits for both firms. Thisse and Vives develop a perfect price discrimination model and assume that one firm has a cost advantage over the other. They show that, in a dominant strategy equilibrium, both firms will choose to price discriminate. The more efficient firm may or may not become better off compared to the non-discriminatory outcome, while the less efficient firm becomes worse off. Shaffer and Zhang (2002) employ a perfect price discrimination model with vertically and horizontally differentiated products. They demonstrate that if the marginal cost of targeting individual consumers is low then both firms offer targeted promotions; if the cost is in an intermediate range, only the larger (high quality) firm offers targeted promotions; and if the cost is high no firm charges more than one price. Rao's results have a similar flavor. Two-group price discrimination with asymmetric firms is taken up in Shaffer and Zhang (2000). Liu and Serfes (2004) examine price competition between two symmetric firms (i.e., pure horizontal differentiation), where, as in the present paper, the level of segmentation depends directly on the underlying precision of customer information. 6 The aim of the present paper is to propose and solve a unifying price discrimination model, with two asymmetric (vertically differentiated) firms, which bridges the gap between the two-group and perfect discrimination paradigms. We show that if the (fixed) cost of information is below a certain threshold, then in the unique Nash equilibrium only the high quality firm acquires information and practices price discrimination. The low quality firm's best response is to credibly commit not to engage in any price discrimination, by not purchasing the customer database (e.g. no haggle, no hassle pricing adopted by Saturn dealers). Interestingly, these strategies constitute an equilibrium irrespective of how refined the information is. The benefits and losses from price discrimination are distributed unevenly between the two firms, with the high quality firm emerging as the only winner. More specifically, equilibrium profits of the high quality firm monotonically increase as the information becomes more refined. In contrast, the profits of the low quality firm monotonically decrease with an increase in the precision of consumer information. Social and consumer welfare are monotonically increasing with respect to the precision of consumer information. Contrary to Corts, who focuses on two-group discrimination and shows that both firms become worse off with price discrimination, we find that when firms have the ability to segment the consumers into more than two groups, the high quality firm becomes better off. Our results demonstrate the robustness of the Shaffer and Zhang (2002) result, that only the high quality firm price discriminates, even if we do not have perfect price discrimination. Finally, our results are in direct contrast to Thisse and Vives, who show that both types of firms will price discriminate. This highlights the importance of the source of firm asymmetry. While Thisse and Vives focus on cost-based asymmetry, we focus on demand side asymmetry. The rest of the paper is organized as follows. The model and the four-stage game is presented in Section 2. The game is analyzed in Section 3. Section 3 also contains the welfare analysis. We summarize in Section 4.

We propose a price discrimination duopoly model with vertically differentiated products to examine the effect of customer-specific information of varying degrees of precision on the equilibrium of a four-stage game. In stage 1, firms choose their product qualities. In stage 2, firms decide whether to acquire consumer information of a given level of precision. We model consumer information as a partition of the characteristics space. A firm who acquires information is able to segment consumers and charge each consumer group a different price. Information of a higher precision is modeled as a partition refinement. Therefore, our modeling framework bridges the gap between the two most studied models in the literature of two-group and perfect price discrimination. In stages 3 and 4 firms compete in prices. We show that the high quality firm always benefits from acquiring information at the expense of its low quality rival. If the cost of the customer database is below a threshold level, then only the high quality firm acquires information and the low quality firm commits to a uniform price. This is the equilibrium outcome regardless of the level of information precision. The equilibrium profits of the high quality firm monotonically increase and those of the low quality firm monotonically decrease as the precision of information improves. Finally, social and consumer welfare monotonically increase with the precision of information.