Optimal Price Discrimination Metrics for Digital Goods

Price discrimination has been ubiquitous in the business world for decades. More recently, advances in information technologies have enabled sellers to collect and store customer information much more cost-e¤ectively. Equipped with analytical tools from burgeoning research in data mining, sellers learn more about each customer’s purchasing pattern, and have begun to personalize prices and product o¤erings to each customer. Amazon.com has experimented with o¤ering di¤erent customers di¤erent prices on DVD titles based on their purchase history. In another example, the Dell Latitude L400 ultralight laptop was listed at $2,307 on the company’s Web page catering to small businesses. On the Web page for sales to health-care companies, the same machine was listed at $2,228, or 3% less. For state and local governments, it was priced at $2,072.04, or 10% less than the price for small businesses. Stimulated by abundant business applications, economists have studied price discrimination extensively for years. Stole (2003) provides a recent survey of price discrimination in the economics literature. However, most of the economic studies focused on price discrimination with one pricing metric, which created a wide gap between the economics and data mining literatures. In the data mining literature, researchers designed various algorithms to discover purchase-decision patterns using a large number of variables. Our multidimensional model attempts to bridge this gap. Also, the economics literature has mainly concentrated on the welfare and consumer-surplus e¤ects of opening new markets or adopting personalized pricing technologies. Few articles discussed the selection of pricing metrics. This is becoming increasingly important, e.g., in the case of enterprise software licensing, whose complexity is growing because of the trend towards licensing software on a subscription or usage basis. However, unlike electricity and gas, the usage of software or server products is not measurable. As a consequence, software vendors are experimenting with di¤erent proxy variables for pricing. The present study develops a model tailored to the metrics selection problem. Our model is related to the menu cost literature (Hanson and Martin, 1990) but the formulation is di¤erent. In practice, the pricing metrics of enterprise software are di¤erent across vendors for similar products, or even for the same product in di¤erent generations. For example, in 2003, Sun Microsystems changed radically to o¤er the Java Enterprise System at a …xed annual cost of $100 per employee. Microsoft introduced per-processor licensing terms for eight server products in 2003. IBM mainframe and complementary products have long been priced based on the horsepower (MIPS) of the hardware. Oracle was …rst priced based on the number of CPUs of the server. They once experimented for two years with licensing based on the speed of the CPU, but abandoned it after Oracle 9i. In 2005, Oracle adjusted its per-CPU licensing to accommodate newly invented multicore chips. Interestingly, di¤erent vendors also treat modern multicore chips di¤erently. Some vendors (e.g. Microsoft SQL Server) price one chip as one CPU whereas the others (e.g. IBM DB2 and Oracle before 2005) price it as multiple CPUs. At the same time, HP, IBM, and Sun are independently developing new usage metrics for on-demand computing (utility computing), and have proposed di¤erent metrics. This phenomenon motivates our research questions: (1) How does the design of an optimal pricing schedule vary with the number and combination of metrics on which pricing is based? (2) How should a seller choose the optimal combination of pricing metrics?