Price Competition and Compatibility in the Presence of Positive Demand Externalities

TLDR

Positive demand externalities mean a consumer’s benefit rises with the number of users, a phenomenon also called network externalities. The study investigates how demand externalities, compatibility, and competition shape the dynamic pricing strategies of incumbents and entrants. The authors use a differential‑game framework, deriving Nash open‑loop optimal price paths. The analysis shows that demand externalities and installed base confer market power, an increasing price trajectory can be optimal in a duopoly durable‑goods market, and both entrants and incumbents benefit from product compatibility—particularly when externalities are strong—while the incumbent profits from compatible entry when the installed base is small.

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.