Price Competition and Compatibility in the Presence of Positive Demand Externalities

Abstract

In many cases, the benefit to a consumer of a product increases with the number of other users of the same product. These demand interdependencies are referred to in the literature as positive demand externalities or network externalities. This paper examines the dynamic pricing behaviors of an incumbent and a later entrant, with special attention to the impacts of demand externalities, compatibility, and competition on prices and profits. Defining market power as the ability to price above a competitor without losing market share, we show how demand externalities and installed base combine to confer market power. We model optimal pricing as a differential game with the optimal price trajectory established as Nash open-loop controls. For a duopoly durable goods market with strong demand externalities, the results show an increasing price trajectory can be optimal. As expected, a new entrant is better off if its products are compatible with those of the incumbent, especially when demand externalities are strong and the installed base of the incumbent is large. Less intuitively, the incumbent as well may be better off agreeing on common standards. The comparison of monopoly and duopoly shows that under strong demand externalities and a small installed base, the incumbent profits from compatible entry.diffusion, new products, dynamic pricing, duopoly competition, network externalities, compatibility, standards

Dynamic Pricing in Management Science

“…This allows him to properly control the robustness of his results, with respect to the various functional forms. This model generalizes many previous contributions and is the basis for many later developments in monopoly and oligopoly settings (Dockner and Jorgensen, 1988;Xie and Sirbu, 1995;Dockner et al, 2000).…”

“…It represents the value of the good to the consumer in monetary terms. If w is distributed randomly in the population (Xie and Sirbu, 1995), following a density function z, the potential market is given by:…”

“…When technological choices are imposed by market forces, dominant firms can achieve compatibility by choosing a technology individually, or collectively if it encourages other businesses to adopt the same technology. Firms may also decide not to make their products compatible (Xie and Sirbu, 1995). Until the issue of compatibility between products is resolved within a given industry, consumers tend to delay their adoption of a technological product.…”

“…Some markets are characterized by the compatibility of their product with others. In this case, the utility a consumer derives from a product also depends on the penetration of compatible products (Xie and Sirbu, 1995). Compatibility issues are particularly important in markets for technological goods where standardization permits the joint use of products, minimizing the need for learning how new products work and reducing the uncertainty associated with new technologies.…”

“…This is especially true for models based on diffusion processes, where introducing expectations would complicate too much the analysis to provide analytical results (Xie and Sirbu, 1995;Dockner et al, 2000). In their purchase decisions, buyers are only sensitive to the current state of the relevant variables, i.e.…”